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Career, 1880–1903 </div> </a> <ul id="toc-Career,_1880–1903-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Personal_life_and_character" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Personal_life_and_character"> <div class="vector-toc-text"> 1.6 Personal life and character </div> </a> <ul id="toc-Personal_life_and_character-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Major_scientific_contributions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Major_scientific_contributions"> <div class="vector-toc-text"> 2 Major scientific contributions </div> </a> <button aria-controls="toc-Major_scientific_contributions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Major scientific contributions subsection </button> <ul id="toc-Major_scientific_contributions-sublist" class="vector-toc-list"> <li id="toc-Chemical_and_electrochemical_thermodynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Chemical_and_electrochemical_thermodynamics"> <div class="vector-toc-text"> 2.1 Chemical and electrochemical thermodynamics </div> </a> <ul id="toc-Chemical_and_electrochemical_thermodynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Statistical_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Statistical_mechanics"> <div class="vector-toc-text"> 2.2 Statistical mechanics </div> </a> <ul id="toc-Statistical_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vector_analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vector_analysis"> <div class="vector-toc-text"> 2.3 Vector analysis </div> </a> <ul id="toc-Vector_analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Physical_optics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Physical_optics"> <div class="vector-toc-text"> 2.4 Physical optics </div> </a> <ul id="toc-Physical_optics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Scientific_recognition" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Scientific_recognition"> <div class="vector-toc-text"> 3 Scientific recognition </div> </a> <ul id="toc-Scientific_recognition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Influence" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Influence"> <div class="vector-toc-text"> 4 Influence </div> </a> <ul id="toc-Influence-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Commemoration" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Commemoration"> <div class="vector-toc-text"> 5 Commemoration </div> </a> <button aria-controls="toc-Commemoration-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Commemoration subsection </button> <ul id="toc-Commemoration-sublist" class="vector-toc-list"> <li id="toc-In_literature" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_literature"> <div class="vector-toc-text"> 5.1 In literature </div> </a> <ul id="toc-In_literature-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gibbs_stamp_(2005)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gibbs_stamp_(2005)"> <div class="vector-toc-text"> 5.2 Gibbs stamp (2005) </div> </a> <ul id="toc-Gibbs_stamp_(2005)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Outline_of_principal_work" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Outline_of_principal_work"> <div class="vector-toc-text"> 6 Outline of principal work </div> </a> <ul id="toc-Outline_of_principal_work-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 7 See also </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 8 References </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle References subsection </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> 8.1 Bibliography </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Primary" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Primary"> <div class="vector-toc-text"> 8.2 Primary </div> </a> <ul id="toc-Primary-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Secondary" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Secondary"> <div class="vector-toc-text"> 8.3 Secondary </div> </a> <ul id="toc-Secondary-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 9 External links </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Josiah Willard Gibbs</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 65 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-65" aria-hidden="true" > 65 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Afrikaans" lang="af" hreflang="af" data-title="Josiah Willard Gibbs" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AC%D9%88%D8%B2%D9%8A%D9%87_%D8%BA%D9%8A%D8%A8%D8%B3" title="جوزيه غيبس – Arabic" lang="ar" hreflang="ar" data-title="جوزيه غيبس" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Willard_Gibbs" title="Willard Gibbs – Aragonese" lang="an" hreflang="an" data-title="Willard Gibbs" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target">Aragonés</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Asturian" lang="ast" hreflang="ast" data-title="Josiah Willard Gibbs" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Cozayya_Uillard_Gibbs" title="Cozayya Uillard Gibbs – Azerbaijani" lang="az" hreflang="az" data-title="Cozayya Uillard Gibbs" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9C%E0%A7%8B%E0%A6%B8%E0%A6%BE%E0%A6%AF%E0%A6%BC%E0%A6%BE_%E0%A6%89%E0%A6%87%E0%A6%B2%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%A1_%E0%A6%97%E0%A6%BF%E0%A6%AC%E0%A6%B8" title="জোসায়া উইলার্ড গিবস – Bangla" lang="bn" hreflang="bn" data-title="জোসায়া উইলার্ড গিবস" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Minnan" lang="nan" hreflang="nan" data-title="Josiah Willard Gibbs" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target">閩南語 / Bân-lâm-gú</a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D0%B6%D0%BE%D0%B7%D0%B0%D1%8F_%D0%A3%D1%96%D0%BB%D0%B0%D1%80%D0%B4_%D0%93%D1%96%D0%B1%D1%81" title="Джозая Уілард Гібс – Belarusian" lang="be" hreflang="be" data-title="Джозая Уілард Гібс" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A3%D0%B8%D0%BB%D0%B0%D1%80%D0%B4_%D0%93%D0%B8%D0%B1%D1%81" title="Уилард Гибс – Bulgarian" lang="bg" hreflang="bg" data-title="Уилард Гибс" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Bosnian" lang="bs" hreflang="bs" data-title="Josiah Willard Gibbs" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Catalan" lang="ca" hreflang="ca" data-title="Josiah Willard Gibbs" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Czech" lang="cs" hreflang="cs" data-title="Josiah Willard Gibbs" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Danish" lang="da" hreflang="da" data-title="Josiah Willard Gibbs" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – German" lang="de" hreflang="de" data-title="Josiah Willard Gibbs" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CE%B6%CE%BF%CF%83%CE%AC%CE%B9%CE%B1_%CE%93%CE%BF%CF%85%CE%AF%CE%BB%CE%B1%CF%81%CE%BD%CF%84_%CE%93%CE%BA%CE%B9%CE%BC%CF%80%CF%82" title="Τζοσάια Γουίλαρντ Γκιμπς – Greek" lang="el" hreflang="el" data-title="Τζοσάια Γουίλαρντ Γκιμπς" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Spanish" lang="es" hreflang="es" data-title="Josiah Willard Gibbs" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Esperanto" lang="eo" hreflang="eo" data-title="Josiah Willard Gibbs" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Basque" lang="eu" hreflang="eu" data-title="Josiah Willard Gibbs" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AC%D9%88%D8%B3%D8%A7%DB%8C%D8%A7_%D9%88%DB%8C%D9%84%D8%A7%D8%B1%D8%AF_%DA%AF%DB%8C%D8%A8%D8%B3" title="جوسایا ویلارد گیبس – Persian" lang="fa" hreflang="fa" data-title="جوسایا ویلارد گیبس" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Willard_Gibbs" title="Willard Gibbs – French" lang="fr" hreflang="fr" data-title="Willard Gibbs" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Irish" lang="ga" hreflang="ga" data-title="Josiah Willard Gibbs" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Galician" lang="gl" hreflang="gl" data-title="Josiah Willard Gibbs" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A1%B0%EC%82%AC%EC%9D%B4%EC%96%B4_%EC%9C%8C%EB%9F%AC%EB%93%9C_%EA%B8%B0%EB%B8%8C%EC%8A%A4" title="조사이어 윌러드 기브스 – Korean" lang="ko" hreflang="ko" data-title="조사이어 윌러드 기브스" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8B%D5%B8%D5%A6%D5%A1%D5%B5%D5%A1_%D4%B3%D5%AB%D5%A2%D5%BD" title="Ջոզայա Գիբս – Armenian" lang="hy" hreflang="hy" data-title="Ջոզայա Գիբս" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Croatian" lang="hr" hreflang="hr" data-title="Josiah Willard Gibbs" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Indonesian" lang="id" hreflang="id" data-title="Josiah Willard Gibbs" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Italian" lang="it" hreflang="it" data-title="Josiah Willard Gibbs" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%27%D7%95%D7%A1%D7%99%D7%94_%D7%95%D7%99%D7%9C%D7%90%D7%A8%D7%93_%D7%92%D7%99%D7%91%D7%A1" title="ג'וסיה וילארד גיבס – Hebrew" lang="he" hreflang="he" data-title="ג'וסיה וילארד גיבס" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%9C%E0%B3%8B%E0%B2%B8%E0%B2%AF%E0%B2%BE_%E0%B2%B5%E0%B2%BF%E0%B2%B2%E0%B2%BE%E0%B2%B0%E0%B3%8D%E0%B2%A1%E0%B3%8D_%E0%B2%97%E0%B2%BF%E0%B2%AC%E0%B3%8D%E0%B2%B8%E0%B3%8D" title="ಜೋಸಯಾ ವಿಲಾರ್ಡ್ ಗಿಬ್ಸ್ – Kannada" lang="kn" hreflang="kn" data-title="ಜೋಸಯಾ ವಿಲಾರ್ಡ್ ಗಿಬ್ಸ್" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target">ಕನ್ನಡ</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%94%D0%B6%D0%BE%D0%B7%D0%B0%D0%B9%D1%8F_%D0%A3%D0%B8%D0%BB%D0%BB%D0%B0%D1%80%D0%B4_%D0%93%D0%B8%D0%B1%D0%B1%D1%81" title="Джозайя Уиллард Гиббс – Kazakh" lang="kk" hreflang="kk" data-title="Джозайя Уиллард Гиббс" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Haitian Creole" lang="ht" hreflang="ht" data-title="Josiah Willard Gibbs" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/D%C5%BEosija_Vil%C4%81rds_Gibss" title="Džosija Vilārds Gibss – Latvian" lang="lv" hreflang="lv" data-title="Džosija Vilārds Gibss" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Lithuanian" lang="lt" hreflang="lt" data-title="Josiah Willard Gibbs" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Hungarian" lang="hu" hreflang="hu" data-title="Josiah Willard Gibbs" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%92%D0%B8%D0%BB%D0%B0%D1%80%D0%B4_%D0%93%D0%B8%D0%B1%D1%81" title="Вилард Гибс – Macedonian" lang="mk" hreflang="mk" data-title="Вилард Гибс" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Willard_Gibbs" title="Willard Gibbs – Malagasy" lang="mg" hreflang="mg" data-title="Willard Gibbs" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target">Malagasy</a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%9C%E0%A5%8B%E0%A4%B8%E0%A4%BF%E0%A4%AF%E0%A4%BE%E0%A4%B9_%E0%A4%B5%E0%A4%BF%E0%A4%B2%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%97%E0%A4%BF%E0%A4%AC%E0%A5%8D%E0%A4%B8" title="जोसियाह विलार्ड गिब्स – Marathi" lang="mr" hreflang="mr" data-title="जोसियाह विलार्ड गिब्स" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target">मराठी</a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%AF%E1%83%9D%E1%83%96%E1%83%90%E1%83%98%E1%83%90_%E1%83%A3%E1%83%98%E1%83%9A%E1%83%90%E1%83%A0%E1%83%93_%E1%83%92%E1%83%98%E1%83%91%E1%83%A1%E1%83%98" title="ჯოზაია უილარდ გიბსი – Mingrelian" lang="xmf" hreflang="xmf" data-title="ჯოზაია უილარდ გიბსი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target">მარგალური</a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AC%D9%88%D8%B2%D9%8A%D9%87_%D8%AC%D9%8A%D8%A8%D8%B3" title="جوزيه جيبس – Egyptian Arabic" lang="arz" hreflang="arz" data-title="جوزيه جيبس" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target">مصرى</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Dutch" lang="nl" hreflang="nl" data-title="Josiah Willard Gibbs" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A6%E3%82%A3%E3%83%A9%E3%83%BC%E3%83%89%E3%83%BB%E3%82%AE%E3%83%96%E3%82%BA" title="ウィラード・ギブズ – Japanese" lang="ja" hreflang="ja" data-title="ウィラード・ギブズ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Josiah Willard Gibbs" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Josiah Willard Gibbs" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Occitan" lang="oc" hreflang="oc" data-title="Josiah Willard Gibbs" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target">Occitan</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Uzbek" lang="uz" hreflang="uz" data-title="Josiah Willard Gibbs" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AC%D9%88%D8%B3%DB%8C%D8%A7_%D9%88%DB%8C%D9%84%D8%A7%D8%B1%D8%AF_%DA%AB%DB%8C%D8%A8%D8%B3" title="جوسیا ویلارد ګیبس – Pashto" lang="ps" hreflang="ps" data-title="جوسیا ویلارد ګیبس" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target">پښتو</a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Piedmontese" lang="pms" hreflang="pms" data-title="Josiah Willard Gibbs" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target">Piemontèis</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Polish" lang="pl" hreflang="pl" data-title="Josiah Willard Gibbs" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Portuguese" lang="pt" hreflang="pt" data-title="Josiah Willard Gibbs" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Romanian" lang="ro" hreflang="ro" data-title="Josiah Willard Gibbs" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%93%D0%B8%D0%B1%D0%B1%D1%81,_%D0%94%D0%B6%D0%BE%D0%B7%D0%B0%D0%B9%D1%8F_%D0%A3%D0%B8%D0%BB%D0%BB%D0%B0%D1%80%D0%B4" title="Гиббс, Джозайя Уиллард – Russian" lang="ru" hreflang="ru" data-title="Гиббс, Джозайя Уиллард" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Willard_Gibbs" title="Willard Gibbs – Slovak" lang="sk" hreflang="sk" data-title="Willard Gibbs" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Slovenian" lang="sl" hreflang="sl" data-title="Josiah Willard Gibbs" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/D%C5%BEosaja_Vilard_Gibs" title="Džosaja Vilard Gibs – Serbian" lang="sr" hreflang="sr" data-title="Džosaja Vilard Gibs" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Finnish" lang="fi" hreflang="fi" data-title="Josiah Willard Gibbs" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/J._Willard_Gibbs" title="J. Willard Gibbs – Swedish" lang="sv" hreflang="sv" data-title="J. Willard Gibbs" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AF%E0%AF%8B%E0%AE%9A%E0%AF%88%E0%AE%AF%E0%AE%BE_%E0%AE%B5%E0%AE%BF%E0%AE%B2%E0%AF%8D%E0%AE%B2%E0%AE%B0%E0%AF%8D%E0%AE%9F%E0%AF%81_%E0%AE%95%E0%AE%BF%E0%AE%AA%E0%AF%8D%E0%AE%9A%E0%AF%81" title="யோசையா வில்லர்டு கிப்சு – Tamil" lang="ta" hreflang="ta" data-title="யோசையா வில்லர்டு கிப்சு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D2%B6%D0%BE%D0%B7%D0%B8%D1%8F_%D0%92%D0%B8%D0%BB%D0%BB%D0%B0%D1%80%D0%B4_%D0%93%D0%B8%D0%B1%D0%B1%D1%81" title="Ҷозия Виллард Гиббс – Tajik" lang="tg" hreflang="tg" data-title="Ҷозия Виллард Гиббс" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target">Тоҷикӣ</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/J._Willard_Gibbs" title="J. Willard Gibbs – Turkish" lang="tr" hreflang="tr" data-title="J. Willard Gibbs" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B6%D0%BE%D0%B7%D0%B0%D1%8F_%D0%92%D1%96%D0%BB%D0%BB%D0%B0%D1%80%D0%B4_%D2%90%D1%96%D0%B1%D0%B1%D0%B7" title="Джозая Віллард Ґіббз – Ukrainian" lang="uk" hreflang="uk" data-title="Джозая Віллард Ґіббз" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D8%AC.%DB%8B%D9%89%D9%84%D9%84%D8%A7%D8%B1%D8%AF_%DA%AF%D9%89%D8%A8%D8%A8%D8%B3" title="ج.ۋىللارد گىببس – Uyghur" lang="ug" hreflang="ug" data-title="ج.ۋىللارد گىببس" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="Uyghur" class="interlanguage-link-target">ئۇيغۇرچە / Uyghurche</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Vietnamese" lang="vi" hreflang="vi" data-title="Josiah Willard Gibbs" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs – Waray" lang="war" hreflang="war" data-title="Josiah Willard Gibbs" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target">Winaray</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%B4%84%E8%A5%BF%E4%BA%9E%C2%B7%E5%A8%81%E6%8B%89%E5%BE%B7%C2%B7%E5%90%89%E5%B8%83%E6%96%AF" title="約西亞·威拉德·吉布斯 – Cantonese" lang="yue" hreflang="yue" data-title="約西亞·威拉德·吉布斯" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zh badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://zh.wikipedia.org/wiki/%E4%B9%94%E8%B5%9B%E4%BA%9A%C2%B7%E5%A8%81%E6%8B%89%E5%BE%B7%C2%B7%E5%90%89%E5%B8%83%E6%96%AF" title="乔赛亚·威拉德·吉布斯 – Chinese" lang="zh" hreflang="zh" data-title="乔赛亚·威拉德·吉布斯" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li> </ul> <div class="after-portlet after-portlet-lang"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q153243#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div 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Click here for more information."><img alt="Featured article" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e7/Cscr-featured.svg/20px-Cscr-featured.svg.png" decoding="async" width="20" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e7/Cscr-featured.svg/30px-Cscr-featured.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e7/Cscr-featured.svg/40px-Cscr-featured.svg.png 2x" data-file-width="466" data-file-height="443" /></a></div></div> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">American scientist (1839–1903)</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For the American linguist and theologian, see <a href="/wiki/Josiah_Willard_Gibbs,_Sr." class="mw-redirect" title="Josiah Willard Gibbs, Sr.">Josiah Willard Gibbs, Sr.</a> For the United States Navy ship, see <a href="/wiki/USNS_Josiah_Willard_Gibbs_(T-AGOR-1)" class="mw-redirect" title="USNS Josiah Willard Gibbs (T-AGOR-1)">USNS Josiah Willard Gibbs (T-AGOR-1)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output 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biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Josiah Willard Gibbs</div></th></tr><tr><td colspan="2" class="infobox-image"><a href="/wiki/File:Josiah_Willard_Gibbs_-from_MMS-.jpg" class="mw-file-description"><img alt="Portrait of Josiah Willard Gibbs" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Josiah_Willard_Gibbs_-from_MMS-.jpg/220px-Josiah_Willard_Gibbs_-from_MMS-.jpg" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Josiah_Willard_Gibbs_-from_MMS-.jpg/330px-Josiah_Willard_Gibbs_-from_MMS-.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Josiah_Willard_Gibbs_-from_MMS-.jpg/440px-Josiah_Willard_Gibbs_-from_MMS-.jpg 2x" data-file-width="888" data-file-height="1184" /></a></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data">(1839-02-11)February 11, 1839 <div style="display:inline" class="birthplace"><a href="/wiki/New_Haven,_Connecticut" title="New Haven, Connecticut">New Haven, Connecticut</a>, U.S.</div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">April 28, 1903(1903-04-28) (aged 64) <div style="display:inline" class="deathplace">New Haven, Connecticut, U.S.</div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category">American</td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/Yale_College" title="Yale College">Yale College</a> (<a href="/wiki/Bachelor_of_Arts" title="Bachelor of Arts">BA</a>, <a href="/wiki/PhD" class="mw-redirect" title="PhD">PhD</a>)</td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><div class="collapsible-list mw-collapsible mw-collapsed" style="text-align: left;"> <div style="line-height: 1.6em; font-weight: bold;"><div>List</div></div> <ul class="mw-collapsible-content" style="margin-top: 0; margin-bottom: 0; line-height: inherit; list-style: none; margin-left: 0;"><li style="line-height: inherit; margin: 0"><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical mechanics</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical thermodynamics</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Chemical_potential" title="Chemical potential">Chemical potential</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Cross_product" title="Cross product">Cross product</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Dyadics" title="Dyadics">Dyadics</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Exergy" title="Exergy">Exergy</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Principle_of_maximum_work" title="Principle of maximum work">Principle of maximum work</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Phase_rule" title="Phase rule">Phase rule</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Phase_space" title="Phase space">Phase space</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Physical_optics" title="Physical optics">Physical optics</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Phase_separation" title="Phase separation">Physics of phase separation</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Statistical_ensemble_(mathematical_physics)" class="mw-redirect" title="Statistical ensemble (mathematical physics)">Statistical ensemble</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Surface_stress" title="Surface stress">Surface stress</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Vector_calculus" title="Vector calculus">Vector calculus</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs_entropy" class="mw-redirect" title="Gibbs entropy">Gibbs entropy</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs_algorithm" title="Gibbs algorithm">Gibbs algorithm</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs_distribution" class="mw-redirect" title="Gibbs distribution">Gibbs distribution</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Surface_rheology" title="Surface rheology">Gibbs' elasticity</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Massieu_function" title="Massieu function">Gibbs function</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs%27_inequality" title="Gibbs' inequality">Gibbs' inequality</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs_isotherm" title="Gibbs isotherm">Gibbs isotherm</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/H-theorem#Gibbs'_H-theorem" title="H-theorem">Gibbs' H theorem</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs_lemma" title="Gibbs lemma">Gibbs lemma</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs_measure" title="Gibbs measure">Gibbs measure</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs_paradox" title="Gibbs paradox">Gibbs paradox</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs_phenomenon" title="Gibbs phenomenon">Gibbs phenomenon</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs_state" title="Gibbs state">Gibbs state</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Maxwell%27s_thermodynamic_surface" title="Maxwell's thermodynamic surface">Gibbs' thermodynamic surface</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Rotation_formalisms_in_three_dimensions#Rodrigues_vector" title="Rotation formalisms in three dimensions">Gibbs vector</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Appell%27s_equation_of_motion" title="Appell's equation of motion">Gibbs–Appell equation of motion</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs%E2%80%93Donnan_effect" title="Gibbs–Donnan effect">Gibbs–Donnan effect</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs%E2%80%93Duhem_equation" title="Gibbs–Duhem equation">Gibbs–Duhem equation</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs%E2%80%93Helmholtz_equation" title="Gibbs–Helmholtz equation">Gibbs–Helmholtz equation</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs%E2%80%93Marangoni_effect" class="mw-redirect" title="Gibbs–Marangoni effect">Gibbs–Marangoni effect</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs%E2%80%93Thomson_equation" title="Gibbs–Thomson equation">Gibbs–Thomson equation</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs%E2%80%93Thomson_effect" class="mw-redirect" title="Gibbs–Thomson effect">Gibbs–Thomson effect</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Wulff_construction" title="Wulff construction">Gibbs–Wulff theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"> <ul><li><a href="/wiki/Rumford_Prize" title="Rumford Prize">Rumford Prize</a> (1880)</li> <li><a href="/wiki/Fellow_of_the_Royal_Society" title="Fellow of the Royal Society">ForMemRS</a> (1897)<a href="#cite_note-formemrs-1">[1]</a></li> <li><a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medal</a> (1901)</li></ul> </div></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546">Scientific career</td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"><ul><li><a href="/wiki/Chemistry" title="Chemistry">Chemistry</a></li><li><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></li><li><a href="/wiki/Physics" title="Physics">Physics</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/Yale_College" title="Yale College">Yale College</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><a rel="nofollow" class="external text" href="http://brbl-dl.library.yale.edu/vufind/Record/3439123">On the form of the teeth of wheels in spur gearing</a> (1863)</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Hubert_Anson_Newton" class="mw-redirect" title="Hubert Anson Newton">Hubert Anson Newton</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><a href="/wiki/Edwin_Bidwell_Wilson" title="Edwin Bidwell Wilson">Edwin Bidwell Wilson</a> <a href="/wiki/Irving_Fisher" title="Irving Fisher">Irving Fisher</a> <a href="/wiki/Henry_Andrews_Bumstead" class="mw-redirect" title="Henry Andrews Bumstead">Henry Andrews Bumstead</a> <a href="/wiki/Lynde_Wheeler" title="Lynde Wheeler">Lynde Wheeler</a> <a href="/wiki/Lee_De_Forest" class="mw-redirect" title="Lee De Forest">Lee De Forest</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th colspan="2" class="infobox-header">Signature</th></tr><tr><td colspan="2" class="infobox-full-data"><a href="/wiki/File:JWgibbs-signature.jpg" class="mw-file-description"><img alt="Gibbs's signature" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/JWgibbs-signature.jpg/150px-JWgibbs-signature.jpg" decoding="async" width="150" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/JWgibbs-signature.jpg/225px-JWgibbs-signature.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/5/5d/JWgibbs-signature.jpg 2x" data-file-width="269" data-file-height="50" /></a></td></tr></tbody></table> Josiah Willard Gibbs (<a href="/wiki/Help:IPA/English" title="Help:IPA/English">/ɡɪbz/</a>;<a href="#cite_note-2">[2]</a> February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a> was instrumental in transforming <a href="/wiki/Physical_chemistry" title="Physical chemistry">physical chemistry</a> into a rigorous deductive science. Together with <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> and <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Ludwig Boltzmann</a>, he created <a href="/wiki/Statistical_mechanics" title="Statistical mechanics">statistical mechanics</a> (a term that he coined), explaining the <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a> as consequences of the statistical properties of <a href="/wiki/Statistical_ensemble_(mathematical_physics)" class="mw-redirect" title="Statistical ensemble (mathematical physics)">ensembles</a> of the possible states of a physical system composed of many particles. Gibbs also worked on the application of <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a> to problems in <a href="/wiki/Physical_optics" title="Physical optics">physical optics</a>. As a mathematician, he created modern <a href="/wiki/Vector_calculus" title="Vector calculus">vector calculus</a> (independently of the British scientist <a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Oliver Heaviside</a>, who carried out similar work during the same period) and described the Gibbs phenomenon in the theory of Fourier analysis. In 1863, <a href="/wiki/Yale_University" title="Yale University">Yale University</a> awarded Gibbs the first American <a href="/wiki/Doctor_of_Philosophy" title="Doctor of Philosophy">doctorate</a> in <a href="/wiki/Engineering" title="Engineering">engineering</a>. After a three-year sojourn in Europe, Gibbs spent the rest of his career at Yale, where he was a professor of <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a> from 1871 until his death in 1903. Working in relative isolation, he became the earliest theoretical scientist in the United States to earn an international reputation and was praised by <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> as "the greatest mind in American history".<a href="#cite_note-APS-3">[3]</a> In 1901, Gibbs received what was then considered the highest honor awarded by the international scientific community, the <a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medal</a> of the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a> of London,<a href="#cite_note-APS-3">[3]</a> "for his contributions to mathematical physics".<a href="#cite_note-Copley-4">[4]</a> Commentators and biographers have remarked on the contrast between Gibbs's quiet, solitary life in turn of the century <a href="/wiki/New_England" title="New England">New England</a> and the great international impact of his ideas. Though his work was almost entirely theoretical, the practical value of Gibbs's contributions became evident with the development of industrial chemistry during the first half of the 20th century. According to <a href="/wiki/Robert_Andrews_Millikan" title="Robert Andrews Millikan">Robert A. Millikan</a>, in pure science, Gibbs "did for statistical mechanics and thermodynamics what <a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Laplace</a> did for celestial mechanics and Maxwell did for electrodynamics, namely, made his field a well-nigh finished theoretical structure".<a href="#cite_note-Millikan-5">[5]</a> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Biography">Biography</h2>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=1" title="Edit section: Biography">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Family_background">Family background</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=2" title="Edit section: Family background">edit</a>]</div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:A_young_Willard_Gibbs.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/A_young_Willard_Gibbs.jpg/170px-A_young_Willard_Gibbs.jpg" decoding="async" width="170" height="259" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/A_young_Willard_Gibbs.jpg/255px-A_young_Willard_Gibbs.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/A_young_Willard_Gibbs.jpg/340px-A_young_Willard_Gibbs.jpg 2x" data-file-width="580" data-file-height="883" /></a><figcaption>Willard Gibbs as a young man</figcaption></figure> Gibbs was born in New Haven, Connecticut. He belonged to an old <a href="/wiki/Yankee" title="Yankee">Yankee</a> family that had produced distinguished American clergymen and academics since the 17th century. He was the fourth of five children and the only son of <a href="/wiki/Josiah_Willard_Gibbs,_Sr." class="mw-redirect" title="Josiah Willard Gibbs, Sr.">Josiah Willard Gibbs Sr.</a>, and his wife Mary Anna, née Van Cleve. On his father's side, he was descended from <a href="/wiki/Samuel_Willard" title="Samuel Willard">Samuel Willard</a>, who served as acting <a href="/wiki/President_of_Harvard_University" title="President of Harvard University">President of Harvard College</a> from 1701 to 1707. On his mother's side, one of his ancestors was the Rev. <a href="/wiki/Jonathan_Dickinson_(New_Jersey_minister)" title="Jonathan Dickinson (New Jersey minister)">Jonathan Dickinson</a>, the first president of the College of New Jersey (later <a href="/wiki/Princeton_University" title="Princeton University">Princeton University</a>). Gibbs's given name, which he shared with his father and several other members of his extended family, derived from his ancestor Josiah Willard, who had been Secretary of the <a href="/wiki/Province_of_Massachusetts_Bay" title="Province of Massachusetts Bay">Province of Massachusetts Bay</a> in the 18th century.<a href="#cite_note-Bumstead-6">[6]</a> His paternal grandmother, Mercy (Prescott) Gibbs, was the sister of <a href="/wiki/Rebecca_Minot_Prescott" title="Rebecca Minot Prescott">Rebecca Minot Prescott</a> Sherman, the wife of American founding father <a href="/wiki/Roger_Sherman" title="Roger Sherman">Roger Sherman</a>; and he was the second cousin of <a href="/wiki/Roger_Sherman_Baldwin" title="Roger Sherman Baldwin">Roger Sherman Baldwin</a>, see the <a href="/wiki/La_Amistad" title="La Amistad">Amistad</a> case below. The elder Gibbs was generally known to his family and colleagues as "Josiah", while the son was called "Willard".<a href="#cite_note-7">[7]</a> Josiah Gibbs was a linguist and theologian who served as professor of sacred literature at <a href="/wiki/Yale_Divinity_School" title="Yale Divinity School">Yale Divinity School</a> from 1824 until his death in 1861. He is chiefly remembered today as the <a href="/wiki/Abolitionism_in_the_United_States" title="Abolitionism in the United States">abolitionist</a> who found an interpreter for the African passengers of the ship <a href="/wiki/La_Amistad" title="La Amistad">Amistad</a>, allowing them to testify during <a href="/wiki/United_States_v._The_Amistad" title="United States v. The Amistad">the trial</a> that followed their rebellion against being sold as slaves.<a href="#cite_note-8">[8]</a> <div class="mw-heading mw-heading3"><h3 id="Education">Education</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=3" title="Edit section: Education">edit</a>]</div> Willard Gibbs was educated at the <a href="/wiki/Hopkins_School" title="Hopkins School">Hopkins School</a> and entered <a href="/wiki/Yale_College" title="Yale College">Yale College</a> in 1854 at the age of 15. At Yale, Gibbs received prizes for excellence in <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> and <a href="/wiki/Latin" title="Latin">Latin</a>, and he graduated in 1858, near the top of his class.<a href="#cite_note-MacTutor-9">[9]</a> He remained at Yale as a graduate student at the <a href="/wiki/Sheffield_Scientific_School" title="Sheffield Scientific School">Sheffield Scientific School</a>. At age 19, soon after his graduation from college, Gibbs was inducted into the <a href="/wiki/Connecticut_Academy_of_Arts_and_Sciences" title="Connecticut Academy of Arts and Sciences">Connecticut Academy of Arts and Sciences</a>, a scholarly institution composed primarily of members of the Yale faculty.<a href="#cite_note-Rukeyser-CTAcademy-10">[10]</a> Relatively few documents from the period survive and it is difficult to reconstruct the details of Gibbs's early career with precision.<a href="#cite_note-Wheeler-college-11">[11]</a> In the opinion of biographers, Gibbs's principal mentor and champion, both at Yale and in the Connecticut Academy, was probably the astronomer and mathematician <a href="/wiki/Hubert_Anson_Newton" class="mw-redirect" title="Hubert Anson Newton">Hubert Anson Newton</a>, a leading authority on <a href="/wiki/Meteoroid" title="Meteoroid">meteors</a>, who remained Gibbs's lifelong friend and confidant.<a href="#cite_note-Rukeyser-CTAcademy-10">[10]</a><a href="#cite_note-Wheeler-college-11">[11]</a> After the death of his father in 1861, Gibbs inherited enough money to make him financially independent.<a href="#cite_note-Rukeyser-inheritance-12">[12]</a> Recurrent <a href="/wiki/Lung" title="Lung">pulmonary</a> trouble ailed the young Gibbs and his physicians were concerned that he might be susceptible to <a href="/wiki/Tuberculosis" title="Tuberculosis">tuberculosis</a>, which had killed his mother. He also suffered from <a href="/wiki/Astigmatism_(eye)" class="mw-redirect" title="Astigmatism (eye)">astigmatism</a>, whose treatment was then still largely unfamiliar to <a href="/wiki/Ophthalmology" title="Ophthalmology">oculists</a>, so that Gibbs had to diagnose himself and grind his own lenses.<a href="#cite_note-Wheeler-astigmatism-13">[13]</a><a href="#cite_note-Rukeyser-astigmatism-14">[14]</a> Though in later years he used <a href="/wiki/Glasses" title="Glasses">glasses</a> only for reading or other close work,<a href="#cite_note-Wheeler-astigmatism-13">[13]</a> Gibbs's delicate health and imperfect eyesight probably explain why he did not volunteer to fight in the <a href="/wiki/American_Civil_War" title="American Civil War">Civil War</a> of 1861–65.<a href="#cite_note-Wheeler-war-15">[15]</a> He was not <a href="/wiki/Conscription_in_the_United_States#Civil_War" title="Conscription in the United States">conscripted</a> and he remained at Yale for the duration of the war.<a href="#cite_note-Rukeyser-war-16">[16]</a> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:JWGibbs-tutor.jpg" class="mw-file-description"><img alt="Portrait of Willard Gibbs as a Yale College tutor" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/JWGibbs-tutor.jpg/170px-JWGibbs-tutor.jpg" decoding="async" width="170" height="214" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/6/68/JWGibbs-tutor.jpg 1.5x" data-file-width="217" data-file-height="273" /></a><figcaption>Gibbs during his time as a tutor at Yale<a href="#cite_note-17">[17]</a></figcaption></figure> In 1863, Gibbs received the first <a href="/wiki/Doctorate_of_Philosophy" class="mw-redirect" title="Doctorate of Philosophy">Doctorate of Philosophy</a> (PhD) in engineering granted in the US, for a thesis entitled "On the Form of the Teeth of Wheels in Spur Gearing", in which he used geometrical techniques to investigate the optimum design for <a href="/wiki/Gear" title="Gear">gears</a>.<a href="#cite_note-MacTutor-9">[9]</a><a href="#cite_note-Wheeler-PhD-18">[18]</a><a href="#cite_note-19">[19]</a> In 1861, Yale had become the first US university to offer a PhD degree<a href="#cite_note-ElmarsafyBernard2013-20">[20]</a> and Gibbs's was only the fifth PhD granted in the US in any subject.<a href="#cite_note-Wheeler-PhD-18">[18]</a> <div class="mw-heading mw-heading3"><h3 id="Career,_1863–1873">Career, 1863–1873</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=4" title="Edit section: Career, 1863–1873">edit</a>]</div> After graduation, Gibbs was appointed as tutor at the college for a term of three years. During the first two years, he taught Latin, and during the third year, he taught "natural philosophy" (i.e., physics).<a href="#cite_note-Bumstead-6">[6]</a> In 1866, he patented a design for a <a href="/wiki/Railway_brake" title="Railway brake">railway brake</a><a href="#cite_note-21">[21]</a> and read a paper before the Connecticut Academy, entitled "The Proper Magnitude of the Units of Length", in which he proposed a scheme for rationalizing the system of units of measurement used in mechanics.<a href="#cite_note-Units-22">[22]</a> After his term as tutor ended, Gibbs traveled to Europe with his sisters. They spent the winter of 1866–67 in Paris, where Gibbs attended lectures at the <a href="/wiki/University_of_Paris" title="University of Paris">Sorbonne</a> and the <a href="/wiki/Coll%C3%A8ge_de_France" title="Collège de France">Collège de France</a>, given by such distinguished mathematical scientists as <a href="/wiki/Joseph_Liouville" title="Joseph Liouville">Joseph Liouville</a> and <a href="/wiki/Michel_Chasles" title="Michel Chasles">Michel Chasles</a>.<a href="#cite_note-23">[23]</a> Having undertaken a punishing regimen of study, Gibbs caught a serious cold and a doctor, fearing tuberculosis, advised him to rest on the <a href="/wiki/French_Riviera" title="French Riviera">Riviera</a>, where he and his sisters spent several months and where he made a full recovery.<a href="#cite_note-24">[24]</a> Moving to <a href="/wiki/Berlin" title="Berlin">Berlin</a>, Gibbs attended the lectures taught by mathematicians <a href="/wiki/Karl_Weierstrass" title="Karl Weierstrass">Karl Weierstrass</a> and <a href="/wiki/Leopold_Kronecker" title="Leopold Kronecker">Leopold Kronecker</a>, as well as by chemist <a href="/wiki/Heinrich_Gustav_Magnus" title="Heinrich Gustav Magnus">Heinrich Gustav Magnus</a>.<a href="#cite_note-25">[25]</a> In August 1867, Gibbs's sister Julia was married in Berlin to <a href="/wiki/Addison_Van_Name" title="Addison Van Name">Addison Van Name</a>, who had been Gibbs's classmate at Yale. The newly married couple returned to New Haven, leaving Gibbs and his sister Anna in Germany.<a href="#cite_note-26">[26]</a> In <a href="/wiki/Heidelberg_University" title="Heidelberg University">Heidelberg</a>, Gibbs was exposed to the work of physicists <a href="/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff">Gustav Kirchhoff</a> and <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a>, and chemist <a href="/wiki/Robert_Bunsen" title="Robert Bunsen">Robert Bunsen</a>. At the time, German academics were the leading authorities in the natural sciences, especially chemistry and <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>.<a href="#cite_note-27">[27]</a> Gibbs returned to Yale in June 1869 and briefly taught French to engineering students.<a href="#cite_note-Klein-proceedings-28">[28]</a> It was probably also around this time that he worked on a new design for a steam-engine <a href="/wiki/Governor_(device)" title="Governor (device)">governor</a>, his last significant investigation in mechanical engineering.<a href="#cite_note-Mayr-29">[29]</a><a href="#cite_note-30">[30]</a> In 1871, he was appointed Professor of Mathematical Physics at Yale, the first such professorship in the United States. Gibbs, who had independent means and had yet to publish anything, was assigned to teach graduate students exclusively and was hired without salary.<a href="#cite_note-Rukeyser-professor-31">[31]</a> <div class="mw-heading mw-heading3"><h3 id="Career,_1873–1880">Career, 1873–1880</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=5" title="Edit section: Career, 1873–1880">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Maxwell%27s_letters_plate_IV.jpg" class="mw-file-description"><img alt="Maxwell's handmade sketch of the thermodynamic surface for water" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Maxwell%27s_letters_plate_IV.jpg/170px-Maxwell%27s_letters_plate_IV.jpg" decoding="async" width="170" height="219" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Maxwell%27s_letters_plate_IV.jpg/255px-Maxwell%27s_letters_plate_IV.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Maxwell%27s_letters_plate_IV.jpg/340px-Maxwell%27s_letters_plate_IV.jpg 2x" data-file-width="418" data-file-height="539" /></a><figcaption>Maxwell's sketch of the lines of constant temperature and pressure, made in preparation for his construction of a solid model based on Gibbs's definition of a thermodynamic surface for water (see <a href="/wiki/Maxwell%27s_thermodynamic_surface" title="Maxwell's thermodynamic surface">Maxwell's thermodynamic surface</a>)</figcaption></figure> Gibbs published his first work in 1873.<a href="#cite_note-MacTutor-9">[9]</a> His papers on the geometric representation of thermodynamic quantities appeared in the Transactions of the Connecticut Academy. These papers introduced the use of different type phase diagrams, which were his favorite aids to the imagination process when doing research, rather than the mechanical models, such as the ones that <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a> used in constructing his electromagnetic theory, which might not completely represent their corresponding phenomena.<a href="#cite_note-32">[32]</a> Although the journal had few readers capable of understanding Gibbs's work, he shared reprints with correspondents in Europe and received an enthusiastic response from <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> at <a href="/wiki/University_of_Cambridge" title="University of Cambridge">Cambridge</a>. Maxwell even made, with his own hands, a <a href="/wiki/Maxwell%27s_thermodynamic_surface" title="Maxwell's thermodynamic surface">clay model illustrating Gibbs's construct</a>. He then produced two plaster casts of his model and mailed one to Gibbs. That cast is on display at the Yale physics department.<a href="#cite_note-33">[33]</a><a href="#cite_note-34">[34]</a> Maxwell included a chapter on Gibbs's work in the next edition of his Theory of Heat, published in 1875. He explained the usefulness of Gibbs's graphical methods in a lecture to the <a href="/wiki/Chemical_Society" title="Chemical Society">Chemical Society</a> of London and even referred to it in the article on "Diagrams" that he wrote for the <a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Encyclopædia Britannica</a>.<a href="#cite_note-35">[35]</a><a href="#cite_note-36">[36]</a> Prospects of collaboration between him and Gibbs were cut short by Maxwell's early death in 1879, aged 48. The joke later circulated in New Haven that "only one man lived who could understand Gibbs's papers. That was Maxwell, and now he is dead."<a href="#cite_note-37">[37]</a> Gibbs then extended his thermodynamic analysis to multi-phase chemical systems (i.e., to systems composed of more than one form of matter) and considered a variety of concrete applications. He described that research in a monograph titled "<a href="/wiki/On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of Heterogeneous Substances</a>", published by the Connecticut Academy in two parts that appeared respectively in 1875 and 1878. That work, which covers about three hundred pages and contains exactly seven hundred numbered mathematical equations,<a href="#cite_note-Cropper-monograph-38">[38]</a> begins with a quotation from <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a> that expresses what would later be called the first and second <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a>: "The <a href="/wiki/Energy" title="Energy">energy</a> of the world is constant. The <a href="/wiki/Entropy" title="Entropy">entropy</a> of the world tends towards a maximum."<a href="#cite_note-39">[39]</a> Gibbs's monograph rigorously and ingeniously applied his thermodynamic techniques to the interpretation of physico-chemical phenomena, explaining and relating what had previously been a mass of isolated facts and observations.<a href="#cite_note-Wheeler-thermodynamics-40">[40]</a> The work has been described as "the <a href="/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica">Principia</a> of thermodynamics" and as a work of "practically unlimited scope".<a href="#cite_note-Cropper-monograph-38">[38]</a> It solidly laid the foundation for physical Chemistry.<a href="#cite_note-Jordan1910-41">[41]</a> <a href="/wiki/Wilhelm_Ostwald" title="Wilhelm Ostwald">Wilhelm Ostwald</a>, who translated Gibbs's monograph into German, referred to Gibbs as the "founder of chemical energetics".<a href="#cite_note-Britannica-1911-42">[42]</a> According to modern commentators, <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"> It is universally recognised that its publication was an event of the first importance in the history of chemistry ... Nevertheless it was a number of years before its value was generally known, this delay was due largely to the fact that its mathematical form and rigorous deductive processes make it difficult reading for anyone, and especially so for students of experimental chemistry whom it most concerns. <div class="templatequotecite">— <cite>J. J. O'Connor and E. F. Robertson, 1997<a href="#cite_note-MacTutor-9">[9]</a></cite></div></blockquote> Gibbs continued to work without pay until 1880, when the new <a href="/wiki/Johns_Hopkins_University" title="Johns Hopkins University">Johns Hopkins University</a> in <a href="/wiki/Baltimore,_Maryland" class="mw-redirect" title="Baltimore, Maryland">Baltimore, Maryland</a> offered him a position paying $3,000 per year. In response, Yale offered him an annual salary of $2,000, which he was content to accept.<a href="#cite_note-43">[43]</a> In 1879, Gibbs derived the <a href="/wiki/Appell%27s_equation_of_motion" title="Appell's equation of motion">Gibbs–Appell equation of motion</a>,<a href="#cite_note-gibbs1879-44">[44]</a> rediscovered in 1900 by <a href="/wiki/Paul_%C3%89mile_Appell" title="Paul Émile Appell">Paul Émile Appell</a>.<a href="#cite_note-appell_1900a-45">[45]</a> <div class="mw-heading mw-heading3"><h3 id="Career,_1880–1903">Career, 1880–1903</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=6" title="Edit section: Career, 1880–1903">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:SloaneLab.jpg" class="mw-file-description"><img alt="Yale University's old Sloane Physical Laboratory" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/SloaneLab.jpg/170px-SloaneLab.jpg" decoding="async" width="170" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/SloaneLab.jpg/255px-SloaneLab.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/67/SloaneLab.jpg/340px-SloaneLab.jpg 2x" data-file-width="410" data-file-height="473" /></a><figcaption>Yale's Sloane Physical Laboratory, as it stood between 1882 and 1931 at the current location of <a href="/wiki/Jonathan_Edwards_College" title="Jonathan Edwards College">Jonathan Edwards College</a>. Gibbs's office was on the second floor, to the right of the tower in the picture.<a href="#cite_note-46">[46]</a></figcaption></figure> From 1880 to 1884, Gibbs worked on developing the <a href="/wiki/Exterior_algebra" title="Exterior algebra">exterior algebra</a> of <a href="/wiki/Hermann_Grassmann" title="Hermann Grassmann">Hermann Grassmann</a> into a <a href="/wiki/Vector_calculus" title="Vector calculus">vector calculus</a> well-suited to the needs of physicists. With this object in mind, Gibbs distinguished between the <a href="/wiki/Dot_product" title="Dot product">dot</a> and <a href="/wiki/Cross_product" title="Cross product">cross products</a> of two vectors and introduced the concept of <a href="/wiki/Dyadics" title="Dyadics">dyadics</a>. Similar work was carried out independently, and at around the same time, by the British mathematical physicist and engineer <a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Oliver Heaviside</a>. Gibbs sought to convince other physicists of the convenience of the vectorial approach over the <a href="/wiki/Quaternion" title="Quaternion">quaternionic</a> calculus of <a href="/wiki/William_Rowan_Hamilton" title="William Rowan Hamilton">William Rowan Hamilton</a>, which was then widely used by British scientists. This led him, in the early 1890s, to a controversy with <a href="/wiki/Peter_Guthrie_Tait" title="Peter Guthrie Tait">Peter Guthrie Tait</a> and others in the pages of <a href="/wiki/Nature_(journal)" title="Nature (journal)">Nature</a>.<a href="#cite_note-Bumstead-6">[6]</a> Gibbs's lecture notes on vector calculus were privately printed in 1881 and 1884 for the use of his students, and were later adapted by <a href="/wiki/Edwin_Bidwell_Wilson" title="Edwin Bidwell Wilson">Edwin Bidwell Wilson</a> into a textbook, <a href="/wiki/Vector_Analysis" title="Vector Analysis">Vector Analysis</a>, published in 1901.<a href="#cite_note-Bumstead-6">[6]</a> That book helped to popularize the "<a href="/wiki/Del" title="Del">del</a>" notation that is widely used today in <a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">electrodynamics</a> and <a href="/wiki/Fluid_mechanics" title="Fluid mechanics">fluid mechanics</a>. In other mathematical work, he re-discovered the "<a href="/wiki/Gibbs_phenomenon" title="Gibbs phenomenon">Gibbs phenomenon</a>" in the theory of <a href="/wiki/Fourier_series" title="Fourier series">Fourier series</a><a href="#cite_note-47">[47]</a> (which, unbeknownst to him and to later scholars, had been described fifty years before by an obscure English mathematician, <a href="/wiki/Henry_Wilbraham" title="Henry Wilbraham">Henry Wilbraham</a>).<a href="#cite_note-48">[48]</a> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Sine_integral.svg" class="mw-file-description"><img alt="Plot of the sine integral" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Sine_integral.svg/220px-Sine_integral.svg.png" decoding="async" width="220" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Sine_integral.svg/330px-Sine_integral.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Sine_integral.svg/440px-Sine_integral.svg.png 2x" data-file-width="359" data-file-height="279" /></a><figcaption>The <a href="/wiki/Sine_integral" class="mw-redirect" title="Sine integral">sine integral</a> function, which gives the overshoot associated with the <a href="/wiki/Gibbs_phenomenon" title="Gibbs phenomenon">Gibbs phenomenon</a> for the Fourier series of a <a href="/wiki/Heaviside_step_function" title="Heaviside step function">step function</a> on the real line</figcaption></figure> From 1882 to 1889, Gibbs wrote five papers on <a href="/wiki/Physical_optics" title="Physical optics">physical optics</a>, in which he investigated <a href="/wiki/Birefringence" title="Birefringence">birefringence</a> and other optical phenomena and defended Maxwell's electromagnetic theory of light against the mechanical theories of <a href="/wiki/William_Thomson,_1st_Baron_Kelvin" class="mw-redirect" title="William Thomson, 1st Baron Kelvin">Lord Kelvin</a> and others.<a href="#cite_note-Bumstead-6">[6]</a> In his work on optics, just as much as in his work on thermodynamics,<a href="#cite_note-Klein1990-49">[49]</a> Gibbs deliberately avoided speculating about the microscopic structure of matter and purposefully confined his research problems to those that can be solved from broad general principles and experimentally confirmed facts. The methods that he used were highly original and the obtained results showed decisively the correctness of Maxwell's electromagnetic theory.<a href="#cite_note-50">[50]</a> Gibbs coined the term statistical mechanics and introduced key concepts in the corresponding mathematical description of physical systems, including the notions of <a href="/wiki/Chemical_potential" title="Chemical potential">chemical potential</a> (1876),<a href="#cite_note-Klein-proceedings-28">[28]</a> and <a href="/wiki/Statistical_ensemble_(mathematical_physics)" class="mw-redirect" title="Statistical ensemble (mathematical physics)">statistical ensemble</a> (1902).<a href="#cite_note-Caldi-51">[51]</a> Gibbs's derivation of the laws of thermodynamics from the statistical properties of systems consisting of many particles was presented in his highly influential textbook Elementary Principles in Statistical Mechanics, published in 1902, a year before his death.<a href="#cite_note-Klein1990-49">[49]</a> Gibbs's retiring personality and intense focus on his work limited his accessibility to students. His principal protégé was Edwin Bidwell Wilson, who nonetheless explained that "except in the classroom I saw very little of Gibbs. He had a way, toward the end of the afternoon, of taking a stroll about the streets between his study in the old Sloane Laboratory and his home—a little exercise between work and dinner—and one might occasionally come across him at that time."<a href="#cite_note-Wilson-reminiscences-52">[52]</a> Gibbs did supervise the doctoral thesis on mathematical economics written by <a href="/wiki/Irving_Fisher" title="Irving Fisher">Irving Fisher</a> in 1891.<a href="#cite_note-Fisher-53">[53]</a> After Gibbs's death, Fisher financed the publication of his Collected Works.<a href="#cite_note-Celebrating-Fisher-54">[54]</a> Another distinguished student was <a href="/wiki/Lee_De_Forest" class="mw-redirect" title="Lee De Forest">Lee De Forest</a>, later a pioneer of radio technology.<a href="#cite_note-DeForest-55">[55]</a> Gibbs died in New Haven on April 28, 1903, at the age of 64, the victim of an acute intestinal obstruction.<a href="#cite_note-Wilson-reminiscences-52">[52]</a> A funeral was conducted two days later at his home on 121 High Street,<a href="#cite_note-56">[56]</a> and his body was buried in the nearby <a href="/wiki/Grove_Street_Cemetery" title="Grove Street Cemetery">Grove Street Cemetery</a>. In May, Yale organized a memorial meeting at the Sloane Laboratory. The eminent British physicist <a href="/wiki/J._J._Thomson" title="J. J. Thomson">J. J. Thomson</a> was in attendance and delivered a brief address.<a href="#cite_note-57">[57]</a> <div class="mw-heading mw-heading3"><h3 id="Personal_life_and_character">Personal life and character</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=7" title="Edit section: Personal life and character">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:JWGibbs.jpg" class="mw-file-description"><img alt="Portrait of Willard Gibbs, circa 1895" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/JWGibbs.jpg/170px-JWGibbs.jpg" decoding="async" width="170" height="234" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/JWGibbs.jpg/255px-JWGibbs.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/JWGibbs.jpg/340px-JWGibbs.jpg 2x" data-file-width="1125" data-file-height="1550" /></a><figcaption>Photograph taken around 1895. According to his student Lynde Wheeler, of the existing portraits, this is the most faithful to Gibbs's kindly habitual expression.<a href="#cite_note-Wheeler-portrait-58">[58]</a></figcaption></figure> Gibbs never married, living all his life in his childhood home with his sister Julia and her husband Addison Van Name, who was the Yale librarian. Except for his customary summer vacations in the <a href="/wiki/Adirondack_Mountains" title="Adirondack Mountains">Adirondacks</a> (at <a href="/wiki/Keene_Valley,_New_York" class="mw-redirect" title="Keene Valley, New York">Keene Valley, New York</a>) and later at the <a href="/wiki/White_Mountains_(New_Hampshire)" class="mw-redirect" title="White Mountains (New Hampshire)">White Mountains</a> (in <a href="/wiki/Intervale,_New_Hampshire" title="Intervale, New Hampshire">Intervale, New Hampshire</a>),<a href="#cite_note-Seeger-gentleman-59">[59]</a> his sojourn in Europe in 1866–1869 was almost the only time that Gibbs spent outside New Haven.<a href="#cite_note-Bumstead-6">[6]</a> He joined Yale's College Church (a <a href="/wiki/Congregational_church" class="mw-redirect" title="Congregational church">Congregational church</a>) at the end of his freshman year<a href="#cite_note-Seeger-gentleman-59">[59]</a><a href="#cite_note-obituary-church-60">[60]</a> and remained a regular attendant for the rest of his life.<a href="#cite_note-Wheeler-views-61">[61]</a> Gibbs generally voted for the <a href="/wiki/Republican_Party_(United_States)" title="Republican Party (United States)">Republican</a> candidate in presidential elections but, like other "<a href="/wiki/Mugwump" class="mw-redirect" title="Mugwump">Mugwumps</a>", his concern over the growing corruption associated with <a href="/wiki/Political_machine" title="Political machine">machine politics</a> led him to support <a href="/wiki/Grover_Cleveland" title="Grover Cleveland">Grover Cleveland</a>, a conservative <a href="/wiki/Democratic_Party_(United_States)" title="Democratic Party (United States)">Democrat</a>, in the <a href="/wiki/1884_United_States_presidential_election" title="1884 United States presidential election">election of 1884</a>.<a href="#cite_note-Samuelson-politics-62">[62]</a> Little else is known of his religious or political views, which he mostly kept to himself.<a href="#cite_note-Wheeler-views-61">[61]</a> Gibbs did not produce a substantial personal correspondence, and many of his letters were later lost or destroyed.<a href="#cite_note-63">[63]</a> Beyond the technical writings concerning his research, he published only two other pieces: a brief obituary for <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a>, one of the founders of the mathematical theory of thermodynamics, and a longer biographical memoir of his mentor at Yale, H. A. Newton.<a href="#cite_note-64">[64]</a> In Edward Bidwell Wilson's view, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"> Gibbs was not an advertiser for personal renown nor a propagandist for science; he was a scholar, scion of an old scholarly family, living before the days when research had become résearch ... Gibbs was not a freak, he had no striking ways, he was a kindly dignified gentleman. <div class="templatequotecite">— <cite>E. B. Wilson, 1931<a href="#cite_note-Wilson-reminiscences-52">[52]</a></cite></div></blockquote> According to <a href="/wiki/Lynde_Wheeler" title="Lynde Wheeler">Lynde Wheeler</a>, who had been Gibbs's student at Yale, in his later years Gibbs <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"> was always neatly dressed, usually wore a felt hat on the street, and never exhibited any of the physical mannerisms or eccentricities sometimes thought to be inseparable from genius ... His manner was cordial without being effusive and conveyed clearly the innate simplicity and sincerity of his nature. <div class="templatequotecite">— <cite>Lynde Wheeler, 1951<a href="#cite_note-Wheeler-portrait-58">[58]</a></cite></div></blockquote> He was a careful investor and financial manager, and at his death in 1903 his estate was valued at $100,000<a href="#cite_note-Seeger-gentleman-59">[59]</a> (roughly $3.39 million today<a href="#cite_note-inflation-US-65">[65]</a>). For many years, he served as trustee, secretary, and treasurer of his alma mater, the Hopkins School.<a href="#cite_note-Wheeler-HopkinsSchool-66">[66]</a> US President <a href="/wiki/Chester_A._Arthur" title="Chester A. Arthur">Chester A. Arthur</a> appointed him as one of the commissioners to the National Conference of Electricians, which convened in <a href="/wiki/Philadelphia" title="Philadelphia">Philadelphia</a> in September 1884, and Gibbs presided over one of its sessions.<a href="#cite_note-Seeger-gentleman-59">[59]</a> A keen and skilled horseman,<a href="#cite_note-67">[67]</a> Gibbs was seen habitually in New Haven driving his sister's <a href="/wiki/Carriage" title="Carriage">carriage</a>.<a href="#cite_note-68">[68]</a> In an obituary published in the <a href="/wiki/American_Journal_of_Science" title="American Journal of Science">American Journal of Science</a>, Gibbs's former student <a href="/wiki/Henry_Andrews_Bumstead" class="mw-redirect" title="Henry Andrews Bumstead">Henry A. Bumstead</a> referred to Gibbs's personal character: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"> Unassuming in manner, genial and kindly in his intercourse with his fellow-men, never showing impatience or irritation, devoid of personal ambition of the baser sort or of the slightest desire to exalt himself, he went far toward realizing the ideal of the unselfish, Christian gentleman. In the minds of those who knew him, the greatness of his intellectual achievements will never overshadow the beauty and dignity of his life. <div class="templatequotecite">— <cite><a href="/wiki/Henry_A._Bumstead" title="Henry A. Bumstead">H. A. Bumstead</a>, 1903<a href="#cite_note-Bumstead-6">[6]</a></cite></div></blockquote> <div class="mw-heading mw-heading2"><h2 id="Major_scientific_contributions">Major scientific contributions</h2>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=8" title="Edit section: Major scientific contributions">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Chemical_and_electrochemical_thermodynamics">Chemical and electrochemical thermodynamics</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=9" title="Edit section: Chemical and electrochemical thermodynamics">edit</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Wykres_Gibbsa.svg" class="mw-file-description"><img alt="Diagram representing the free energy of a substance" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Wykres_Gibbsa.svg/250px-Wykres_Gibbsa.svg.png" decoding="async" width="250" height="288" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Wykres_Gibbsa.svg/375px-Wykres_Gibbsa.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Wykres_Gibbsa.svg/500px-Wykres_Gibbsa.svg.png 2x" data-file-width="695" data-file-height="800" /></a><figcaption>Graphical representation of the free energy of a body, from the latter of the papers published by Gibbs in 1873. This shows a plane of constant volume, passing through the point A that represents the body's initial state. The curve MN is the section of the "surface of dissipated energy". AD and AE are, respectively, the energy (ε) and entropy (η) of the initial state. AB is the "available energy" (now called the <a href="/wiki/Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz free energy</a>) and AC the "capacity for entropy" (i.e., the amount by which the entropy can be increased without changing the energy or volume).</figcaption></figure> Gibbs's papers from the 1870s introduced the idea of expressing the internal energy U of a system in terms of the <a href="/wiki/Entropy" title="Entropy">entropy</a> S, in addition to the usual <a href="/wiki/State_variable" title="State variable">state variables</a> of volume V, pressure p, and temperature T. He also introduced the concept of the <a href="/wiki/Chemical_potential" title="Chemical potential">chemical potential</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"> of a given chemical species, defined to be the rate of the increase in U associated with the increase in the number N of molecules of that species (at constant entropy and volume). Thus, it was Gibbs who first combined the first and second <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a> by expressing the infinitesimal change in the internal energy, dU, of a <a href="/wiki/Closed_system" title="Closed system">closed system</a> in the form<a href="#cite_note-Klein1990-49">[49]</a> <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U=T\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>=</mo> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>−</mo> <mi>p</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>+</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U=T\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87c34859595eb1acad708381992945d716ba633c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:31.854ex; height:5.509ex;" alt="{\displaystyle \mathrm {d} U=T\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\,\mathrm {d} N_{i},}"></dd></dl> where T is the <a href="/wiki/Absolute_temperature" class="mw-redirect" title="Absolute temperature">absolute temperature</a>, p is the pressure, dS is an infinitesimal change in entropy and dV is an infinitesimal change of volume. The last term is the sum, over all the chemical species in a chemical reaction, of the chemical potential, μi, of the i-th species, multiplied by the infinitesimal change in the number of moles, dNi of that species. By taking the <a href="/wiki/Legendre_transformation" title="Legendre transformation">Legendre transform</a> of this expression, he defined the concepts of <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a> H and <a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a> G: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{(p,T)}=H-TS.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>=</mo> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{(p,T)}=H-TS.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e442fbdca562c0513650465f836148324db3c3b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:17.564ex; height:3.009ex;" alt="{\displaystyle G_{(p,T)}=H-TS.}"></dd></dl> This compares to the expression for <a href="/wiki/Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz free energy</a> A: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{(v,T)}=U-TS.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>v</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>=</mo> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{(v,T)}=U-TS.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd81550576326abae126ec3960eee3d1bdb5a5f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:17.17ex; height:3.009ex;" alt="{\displaystyle A_{(v,T)}=U-TS.}"></dd></dl> When the Gibbs free energy for a chemical reaction is negative, the reaction will proceed spontaneously. When a chemical system is at <a href="/wiki/Equilibrium_chemistry" title="Equilibrium chemistry">equilibrium</a>, the change in Gibbs free energy is zero. An <a href="/wiki/Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a> is simply related to the free energy change when the reactants are in their <a href="/wiki/Standard_state" title="Standard state">standard states</a>: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta G^{\ominus }=-RT\ln K^{\ominus }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡</mo> <msup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊖</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta G^{\ominus }=-RT\ln K^{\ominus }.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1f22f0afa0c233a5725aad1def46c257fb27bfb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:20.545ex; height:2.676ex;" alt="{\displaystyle \Delta G^{\ominus }=-RT\ln K^{\ominus }.}"></dd></dl> <a href="/wiki/Chemical_potential" title="Chemical potential">Chemical potential</a> is usually defined as partial molar Gibbs free energy: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>P</mi> <mo>,</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>≠</mo> <mi>i</mi> </mrow> </msub> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i}}.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5c3fffb7584ace379b0009767409f99f7fc1a31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:21.259ex; height:6.843ex;" alt="{\displaystyle \mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i}}.}"></dd></dl> Gibbs also obtained what later came to be known as the "<a href="/wiki/Gibbs%E2%80%93Duhem_equation" title="Gibbs–Duhem equation">Gibbs–Duhem equation</a>".<a href="#cite_note-Ott-69">[69]</a> In an <a href="/wiki/Electrochemistry" title="Electrochemistry">electrochemical reaction</a> characterized by an <a href="/wiki/Electromotive_force" title="Electromotive force">electromotive force</a> ℰ and an amount of transferred charge Q, Gibbs's starting equation becomes <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U=T\mathrm {d} S-p\,\mathrm {d} V+{\mathcal {E}}\mathrm {d} Q.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>=</mo> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>−</mo> <mi>p</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>Q</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U=T\mathrm {d} S-p\,\mathrm {d} V+{\mathcal {E}}\mathrm {d} Q.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c238e3cb323fd163448212e564668b8784a4b620" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:26.007ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} U=T\mathrm {d} S-p\,\mathrm {d} V+{\mathcal {E}}\mathrm {d} Q.}"></dd></dl> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Apparatus_for_investigating_the_Phase_Rule_of_an_iron-nitrogen_system_9p290969x.tif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Apparatus_for_investigating_the_Phase_Rule_of_an_iron-nitrogen_system_9p290969x.tif/lossless-page1-220px-Apparatus_for_investigating_the_Phase_Rule_of_an_iron-nitrogen_system_9p290969x.tif.png" decoding="async" width="220" height="174" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Apparatus_for_investigating_the_Phase_Rule_of_an_iron-nitrogen_system_9p290969x.tif/lossless-page1-330px-Apparatus_for_investigating_the_Phase_Rule_of_an_iron-nitrogen_system_9p290969x.tif.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Apparatus_for_investigating_the_Phase_Rule_of_an_iron-nitrogen_system_9p290969x.tif/lossless-page1-440px-Apparatus_for_investigating_the_Phase_Rule_of_an_iron-nitrogen_system_9p290969x.tif.png 2x" data-file-width="3226" data-file-height="2553" /></a><figcaption>Apparatus for investigating the phase rule of an iron–nitrogen system, U.S. Fixed Nitrogen Research Laboratory, 1930</figcaption></figure> The publication of the paper "<a href="/wiki/On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of Heterogeneous Substances</a>" (1874–1878) is now regarded as a landmark in the development of <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>.<a href="#cite_note-MacTutor-9">[9]</a> In it, Gibbs developed a rigorous mathematical theory for various <a href="/wiki/Transport_phenomena" title="Transport phenomena">transport phenomena</a>, including <a href="/wiki/Adsorption" title="Adsorption">adsorption</a>, <a href="/wiki/Electrochemistry" title="Electrochemistry">electrochemistry</a>, and the <a href="/wiki/Marangoni_effect" title="Marangoni effect">Marangoni effect</a> in fluid mixtures.<a href="#cite_note-Wheeler-thermodynamics-40">[40]</a> He also formulated the <a href="/wiki/Phase_rule" title="Phase rule">phase rule</a> <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=C-P+2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>C</mi> <mo>−</mo> <mi>P</mi> <mo>+</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=C-P+2}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/223a97115f60477e71af4dfcef51b67ce833f6d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:15.194ex; height:2.343ex;" alt="{\displaystyle F=C-P+2}"></dd></dl> for the number F of <a href="/wiki/Intensive_and_extensive_properties" title="Intensive and extensive properties">variables</a> that may be independently controlled in an equilibrium mixture of C components existing in P <a href="/wiki/Phase_(matter)" title="Phase (matter)">phases</a>. The phase rule is very useful in diverse areas, such as metallurgy, mineralogy, and petrology. It can also be applied to various research problems in physical chemistry.<a href="#cite_note-70">[70]</a> <div class="mw-heading mw-heading3"><h3 id="Statistical_mechanics">Statistical mechanics</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=10" title="Edit section: Statistical mechanics">edit</a>]</div> Together with <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> and <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Ludwig Boltzmann</a>, Gibbs founded "statistical mechanics", a term that he coined to identify the branch of theoretical physics that accounts for the observed thermodynamic properties of systems in terms of the statistics of <a href="/wiki/Statistical_ensemble_(mathematical_physics)" class="mw-redirect" title="Statistical ensemble (mathematical physics)">ensembles</a> of all possible physical states of a system composed of many particles. He introduced the concept of "<a href="/wiki/Phase_space" title="Phase space">phase of a mechanical system</a>".<a href="#cite_note-Nolte2010-71">[71]</a><a href="#cite_note-72">[72]</a> He used the concept to define the <a href="/wiki/Microcanonical_ensemble" title="Microcanonical ensemble">microcanonical</a>, <a href="/wiki/Canonical_ensemble" title="Canonical ensemble">canonical</a>, and <a href="/wiki/Grand_canonical_ensemble" title="Grand canonical ensemble">grand canonical ensembles</a>; all related to the <a href="/wiki/Gibbs_measure" title="Gibbs measure">Gibbs measure</a>, thus obtaining a more general formulation of the statistical properties of many-particle systems than Maxwell and Boltzmann had achieved before him.<a href="#cite_note-73">[73]</a> Gibbs generalized Boltzmann's statistical interpretation of <a href="/wiki/Entropy" title="Entropy">entropy</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"> by defining the entropy of an arbitrary ensemble as <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S=-k_{\text{B}}\,\sum _{i}p_{i}\ln p_{i},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>B</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=-k_{\text{B}}\,\sum _{i}p_{i}\ln p_{i},}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90d6407cea8cb0c83240643f9ffd9dd3056eed3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:20.828ex; height:5.509ex;" alt="{\displaystyle S=-k_{\text{B}}\,\sum _{i}p_{i}\ln p_{i},}"></dd></dl> where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{\text{B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>B</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{\text{B}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9582c7c795d2def2c061f0dfa3a6f0fb3dd2de44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.607ex; height:2.509ex;" alt="{\displaystyle k_{\text{B}}}"> is the <a href="/wiki/Boltzmann_constant" title="Boltzmann constant">Boltzmann constant</a>, while the sum is over all possible <a href="/wiki/Microstate_(statistical_mechanics)" title="Microstate (statistical mechanics)">microstates</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}">, with <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bab39399bf5424f25d957cdc57c84a0622626d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.059ex; height:2.009ex;" alt="{\displaystyle p_{i}}"> the corresponding probability of the microstate (see <a href="/wiki/Entropy_(statistical_thermodynamics)#Gibbs_entropy_formula" title="Entropy (statistical thermodynamics)">Gibbs entropy formula</a>).<a href="#cite_note-jaynes1965-74">[74]</a> This same formula would later play a central role in <a href="/wiki/Claude_Shannon" title="Claude Shannon">Claude Shannon</a>'s <a href="/wiki/Information_theory" title="Information theory">information theory</a> and is therefore often seen as the basis of the modern information-theoretical interpretation of thermodynamics.<a href="#cite_note-Reif-75">[75]</a> According to <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a>, writing in 1904, even though Maxwell and Boltzmann had previously explained the <a href="/wiki/Irreversible_process" title="Irreversible process">irreversibility</a> of macroscopic physical processes in probabilistic terms, "the one who has seen it most clearly, in a book too little read because it is a little difficult to read, is Gibbs, in his Elementary Principles of Statistical Mechanics".<a href="#cite_note-Poincare-76">[76]</a> Gibbs's analysis of irreversibility, and his formulation of Boltzmann's <a href="/wiki/H-theorem" title="H-theorem">H-theorem</a> and of the <a href="/wiki/Ergodic_hypothesis" title="Ergodic hypothesis">ergodic hypothesis</a>, were major influences on the mathematical physics of the 20th century.<a href="#cite_note-Wightman-77">[77]</a><a href="#cite_note-Wiener-78">[78]</a> Gibbs was well aware that the application of the <a href="/wiki/Equipartition_theorem" title="Equipartition theorem">equipartition theorem</a> to large systems of classical particles failed to explain the measurements of the <a href="/wiki/Heat_capacity" title="Heat capacity">specific heats</a> of both solids and gases, and he argued that this was evidence of the danger of basing thermodynamics on "hypotheses about the constitution of matter".<a href="#cite_note-Klein1990-49">[49]</a> Gibbs's own framework for statistical mechanics, based on ensembles of macroscopically indistinguishable <a href="/wiki/Microstate_(statistical_mechanics)" title="Microstate (statistical mechanics)">microstates</a>, could be carried over almost intact after the discovery that the microscopic laws of nature obey quantum rules, rather than the classical laws known to Gibbs and to his contemporaries.<a href="#cite_note-MacTutor-9">[9]</a><a href="#cite_note-79">[79]</a> His resolution of the so-called "<a href="/wiki/Gibbs_paradox" title="Gibbs paradox">Gibbs paradox</a>", about the entropy of the mixing of gases, is now often cited as a prefiguration of the <a href="/wiki/Identical_particles" class="mw-redirect" title="Identical particles">indistinguishability of particles</a> required by quantum physics.<a href="#cite_note-80">[80]</a> <div class="mw-heading mw-heading3"><h3 id="Vector_analysis">Vector analysis</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=11" title="Edit section: Vector analysis">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Cross_product_parallelogram.svg" class="mw-file-description"><img alt="Diagram representing the cross product of two vectors" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Cross_product_parallelogram.svg/220px-Cross_product_parallelogram.svg.png" decoding="async" width="220" height="164" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Cross_product_parallelogram.svg/330px-Cross_product_parallelogram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Cross_product_parallelogram.svg/440px-Cross_product_parallelogram.svg.png 2x" data-file-width="794" data-file-height="593" /></a><figcaption>Diagram showing the magnitude and direction of the cross product of two vectors, in the notation introduced by Gibbs</figcaption></figure> British scientists, including Maxwell, had relied on Hamilton's <a href="/wiki/Quaternion" title="Quaternion">quaternions</a> in order to express the dynamics of physical quantities, like the electric and magnetic fields, having both a magnitude and a direction in three-dimensional space. Following <a href="/wiki/W._K._Clifford" class="mw-redirect" title="W. K. Clifford">W. K. Clifford</a> in his <a href="/wiki/Elements_of_Dynamic" title="Elements of Dynamic">Elements of Dynamic</a> (1888), Gibbs noted that the product of quaternions could be separated into two parts: a one-dimensional (scalar) quantity and a three-dimensional <a href="/wiki/Euclidean_vector" title="Euclidean vector">vector</a>, so that the use of quaternions involved mathematical complications and redundancies that could be avoided in the interest of simplicity and to facilitate teaching. In his Yale classroom notes he defined distinct dot and cross products for pairs of vectors and introduced the now common notation for them. Through the 1901 textbook <a href="/wiki/Vector_Analysis" title="Vector Analysis">Vector Analysis</a> prepared by <a href="/wiki/Edwin_Bidwell_Wilson" title="Edwin Bidwell Wilson">E. B. Wilson</a> from Gibbs notes, he was largely responsible for the development of the <a href="/wiki/Vector_calculus" title="Vector calculus">vector calculus</a> techniques still used today in electrodynamics and fluid mechanics.<a href="#cite_note-81">[81]</a> While he was working on vector analysis in the late 1870s, Gibbs discovered that his approach was similar to the one that Grassmann had taken in his "multiple algebra".<a href="#cite_note-Grassmann-algebra-82">[82]</a> Gibbs then sought to publicize Grassmann's work, stressing that it was both more general and historically prior to Hamilton's quaternionic algebra. To establish priority of Grassmann's ideas, Gibbs convinced Grassmann's heirs to seek the publication in Germany of the essay "Theorie der Ebbe und Flut" on <a href="/wiki/Tide" title="Tide">tides</a> that Grassmann had submitted in 1840 to the faculty at the <a href="/wiki/University_of_Berlin" class="mw-redirect" title="University of Berlin">University of Berlin</a>, in which he had first introduced the notion of what would later be called a <a href="/wiki/Vector_space" title="Vector space">vector space</a> (<a href="/wiki/Linear_space" class="mw-redirect" title="Linear space">linear space</a>).<a href="#cite_note-Grassmann-tides-83">[83]</a><a href="#cite_note-MacTutor_Grassmann-84">[84]</a> As Gibbs had advocated in the 1880s and 1890s, quaternions were eventually all but abandoned by physicists in favor of the vectorial approach developed by him and, independently, by <a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Oliver Heaviside</a>. Gibbs applied his vector methods to the determination of planetary and comet <a href="/wiki/Orbit" title="Orbit">orbits</a>.<a href="#cite_note-Crowe1967-85">[85]</a>: 160  He also developed the concept of mutually reciprocal triads of vectors that later proved to be of importance in <a href="/wiki/Crystallography" title="Crystallography">crystallography</a>.<a href="#cite_note-86">[86]</a> <div class="mw-heading mw-heading3"><h3 id="Physical_optics">Physical optics</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=12" title="Edit section: Physical optics">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Calcite.jpg" class="mw-file-description"><img alt="Photograph showing birefrigence by a calcite crystal" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Calcite.jpg/220px-Calcite.jpg" decoding="async" width="220" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Calcite.jpg/330px-Calcite.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Calcite.jpg/440px-Calcite.jpg 2x" data-file-width="750" data-file-height="329" /></a><figcaption>A <a href="/wiki/Calcite" title="Calcite">calcite</a> crystal produces birefringence (or "double refraction") of light, a phenomenon which Gibbs explained using Maxwell's equations for electromagnetic phenomena.</figcaption></figure> Though Gibbs's research on physical optics is less well known today than his other work, it made a significant contribution to classical <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> by applying <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a> to the theory of optical processes such as <a href="/wiki/Birefringence" title="Birefringence">birefringence</a>, <a href="/wiki/Dispersion_(optics)" title="Dispersion (optics)">dispersion</a>, and <a href="/wiki/Optical_rotation" title="Optical rotation">optical activity</a>.<a href="#cite_note-Bumstead-6">[6]</a><a href="#cite_note-Optics-87">[87]</a> In that work, Gibbs showed that those processes could be accounted for by Maxwell's equations without any special assumptions about the microscopic structure of matter or about the nature of the medium in which electromagnetic waves were supposed to propagate (the so-called <a href="/wiki/Luminiferous_aether" title="Luminiferous aether">luminiferous ether</a>). Gibbs also stressed that the absence of a <a href="/wiki/Longitudinal_wave" title="Longitudinal wave">longitudinal</a> electromagnetic wave, which is needed to account for the observed properties of <a href="/wiki/Light" title="Light">light</a>, is automatically guaranteed by Maxwell's equations (by virtue of what is now called their "<a href="/wiki/Gauge_fixing" title="Gauge fixing">gauge invariance</a>"), whereas in mechanical theories of light, such as Lord Kelvin's, it must be imposed as an ad hoc condition on the properties of the aether.<a href="#cite_note-Optics-87">[87]</a> In his last paper on physical optics, Gibbs concluded that <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote">it may be said for the electrical theory [of light] that it is not obliged to invent hypotheses, but only to apply the laws furnished by the science of electricity, and that it is difficult to account for the coincidences between the electrical and optical properties of media unless we regard the motions of light as electrical.<div class="templatequotecite">— <cite>J. W. Gibbs, 1889<a href="#cite_note-Bumstead-6">[6]</a></cite></div></blockquote> Shortly afterwards, the electromagnetic nature of light was demonstrated by the experiments of <a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Heinrich Hertz</a> in Germany.<a href="#cite_note-Hertz-88">[88]</a> <div class="mw-heading mw-heading2"><h2 id="Scientific_recognition">Scientific recognition</h2>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=13" title="Edit section: Scientific recognition">edit</a>]</div> Gibbs worked at a time when there was little tradition of rigorous theoretical science in the United States. His research was not easily understandable to his students or his colleagues, and he made no effort to popularize his ideas or to simplify their exposition to make them more accessible.<a href="#cite_note-MacTutor-9">[9]</a> His seminal work on thermodynamics was published mostly in the Transactions of the Connecticut Academy, a journal edited by his librarian brother-in-law, which was little read in the US and even less so in Europe. When Gibbs submitted his long paper on the equilibrium of heterogeneous substances to the academy, both <a href="/wiki/Elias_Loomis" title="Elias Loomis">Elias Loomis</a> and H. A. Newton protested that they did not understand Gibbs's work at all, but they helped to raise the money needed to pay for the typesetting of the many mathematical symbols in the paper. Several Yale faculty members, as well as business and professional men in New Haven, contributed funds for that purpose.<a href="#cite_note-Rukeyser-printing-89">[89]</a> Even though it had been immediately embraced by Maxwell, Gibbs's graphical formulation of the laws of thermodynamics came into widespread use only in the mid 20th century, with the work of <a href="/wiki/L%C3%A1szl%C3%B3_Tisza" title="László Tisza">László Tisza</a> and <a href="/wiki/Herbert_Callen" title="Herbert Callen">Herbert Callen</a>.<a href="#cite_note-90">[90]</a> According to James Gerald Crowther, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote">in his later years [Gibbs] was a tall, dignified gentleman, with a healthy stride and ruddy complexion, performing his share of household chores, approachable and kind (if unintelligible) to students. Gibbs was highly esteemed by his friends, but American science was too preoccupied with practical questions to make much use of his profound theoretical work during his lifetime. He lived out his quiet life at Yale, deeply admired by a few able students but making no immediate impress on American science commensurate with his genius.<div class="templatequotecite">— <cite>J. G. Crowther, 1937<a href="#cite_note-MacTutor-9">[9]</a></cite></div></blockquote> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Burlington_House_ILN_1873.jpg" class="mw-file-description"><img alt="Image of Burlington House, London, in 1873" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Burlington_House_ILN_1873.jpg/220px-Burlington_House_ILN_1873.jpg" decoding="async" width="220" height="151" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Burlington_House_ILN_1873.jpg/330px-Burlington_House_ILN_1873.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Burlington_House_ILN_1873.jpg/440px-Burlington_House_ILN_1873.jpg 2x" data-file-width="600" data-file-height="413" /></a><figcaption><a href="/wiki/Burlington_House" title="Burlington House">Burlington House</a>, site of the Royal Society of London, in 1873</figcaption></figure> On the other hand, Gibbs did receive the major honors then possible for an academic scientist in the US. He was elected to the <a href="/wiki/National_Academy_of_Sciences" title="National Academy of Sciences">National Academy of Sciences</a> in 1879 and received the 1880 <a href="/wiki/Rumford_Prize" title="Rumford Prize">Rumford Prize</a> from the <a href="/wiki/American_Academy_of_Arts_and_Sciences" title="American Academy of Arts and Sciences">American Academy of Arts and Sciences</a> for his work on chemical thermodynamics.<a href="#cite_note-91">[91]</a> In 1895, he was elected to the <a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a> in 1895.<a href="#cite_note-92">[92]</a> He was also awarded honorary doctorates by Princeton University and <a href="/wiki/Williams_College" title="Williams College">Williams College</a>.<a href="#cite_note-Bumstead-6">[6]</a> In Europe, Gibbs was inducted as honorary member of the <a href="/wiki/London_Mathematical_Society" title="London Mathematical Society">London Mathematical Society</a> in 1892 and elected <a href="/wiki/List_of_Fellows_of_the_Royal_Society_elected_in_1897" class="mw-redirect" title="List of Fellows of the Royal Society elected in 1897">Foreign Member of the Royal Society in 1897</a>.<a href="#cite_note-formemrs-1">[1]</a> He was elected as corresponding member of the <a href="/wiki/Prussian_Academy_of_Sciences" title="Prussian Academy of Sciences">Prussian</a> and <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French</a> Academies of Science and received honorary doctorates from the universities of <a href="/wiki/University_of_Dublin" title="University of Dublin">Dublin</a>,<a href="#cite_note-93">[93]</a> <a href="/wiki/University_of_Erlangen-Nuremberg" class="mw-redirect" title="University of Erlangen-Nuremberg">Erlangen</a>, and <a href="/wiki/University_of_Oslo" title="University of Oslo">Christiania</a><a href="#cite_note-Bumstead-6">[6]</a> (now Oslo). The Royal Society further honored Gibbs in 1901 with the <a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medal</a>, then regarded as the highest international award in the natural sciences,<a href="#cite_note-APS-3">[3]</a> noting that he had been "the first to apply the second law of thermodynamics to the exhaustive discussion of the relation between chemical, electrical and thermal energy and capacity for external work."<a href="#cite_note-Britannica-1911-42">[42]</a> Gibbs, who remained in New Haven, was represented at the award ceremony by Commander <a href="/wiki/Richardson_Clover" title="Richardson Clover">Richardson Clover</a>, the US naval attaché in London.<a href="#cite_note-94">[94]</a> In his autobiography, mathematician <a href="/wiki/Gian-Carlo_Rota" title="Gian-Carlo Rota">Gian-Carlo Rota</a> tells of casually browsing the mathematical stacks of <a href="/wiki/Sterling_Library" class="mw-redirect" title="Sterling Library">Sterling Library</a> and stumbling on a handwritten mailing list, attached to some of Gibbs's course notes, which listed over two hundred notable scientists of his day, including Poincaré, Boltzmann, <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a>, and <a href="/wiki/Ernst_Mach" title="Ernst Mach">Ernst Mach</a>. From this, Rota concluded that Gibbs's work was better known among the scientific elite of his day than the published material suggests.<a href="#cite_note-Rota-95">[95]</a> Lynde Wheeler reproduces that mailing list in an appendix to his biography of Gibbs.<a href="#cite_note-Wheeler-mailing-96">[96]</a> That Gibbs succeeded in interesting his European correspondents in his work is demonstrated by the fact that his monograph "On the Equilibrium of Heterogeneous Substances" was translated into German (then the leading language for chemistry) by <a href="/wiki/Wilhelm_Ostwald" title="Wilhelm Ostwald">Wilhelm Ostwald</a> in 1892 and into French by <a href="/wiki/Henri_Louis_Le_Ch%C3%A2telier" class="mw-redirect" title="Henri Louis Le Châtelier">Henri Louis Le Châtelier</a> in 1899.<a href="#cite_note-97">[97]</a> <div class="mw-heading mw-heading2"><h2 id="Influence">Influence</h2>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=14" title="Edit section: Influence">edit</a>]</div> Gibbs's most immediate and obvious influence was on physical chemistry and statistical mechanics, two disciplines which he greatly helped to found. During Gibbs's lifetime, his phase rule was experimentally validated by Dutch chemist <a href="/wiki/Hendrik_Willem_Bakhuis_Roozeboom" title="Hendrik Willem Bakhuis Roozeboom">H. W. Bakhuis Roozeboom</a>, who showed how to apply it in a variety of situations, thereby assuring it of widespread use.<a href="#cite_note-Roozeboom-98">[98]</a> In industrial chemistry, Gibbs's thermodynamics found many applications during the early 20th century, from electrochemistry to the development of the <a href="/wiki/Haber_process" title="Haber process">Haber process</a> for the synthesis of <a href="/wiki/Ammonia" title="Ammonia">ammonia</a>.<a href="#cite_note-Haber-99">[99]</a> When Dutch physicist <a href="/wiki/Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">J. D. van der Waals</a> received the 1910 <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize</a> "for his work on the <a href="/wiki/Equation_of_state" title="Equation of state">equation of state</a> for gases and liquids" he acknowledged the great influence of Gibbs's work on that subject.<a href="#cite_note-vanderWaals-100">[100]</a> <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a> received the 1918 Nobel Prize for his work on quantum mechanics, particularly his 1900 paper on <a href="/wiki/Planck%27s_law" title="Planck's law">Planck's law</a> for quantized <a href="/wiki/Black-body_radiation" title="Black-body radiation">black-body radiation</a>. That work was based largely on the thermodynamics of Kirchhoff, Boltzmann, and Gibbs. Planck declared that Gibbs's name "not only in America but in the whole world will ever be reckoned among the most renowned theoretical physicists of all times."<a href="#cite_note-Planck-101">[101]</a> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Gibbs-Elementary_principles_in_statistical_mechanics.png" class="mw-file-description"><img alt="Title page of Gibbs's Statistical Mechanics" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Gibbs-Elementary_principles_in_statistical_mechanics.png/170px-Gibbs-Elementary_principles_in_statistical_mechanics.png" decoding="async" width="170" height="271" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Gibbs-Elementary_principles_in_statistical_mechanics.png/255px-Gibbs-Elementary_principles_in_statistical_mechanics.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Gibbs-Elementary_principles_in_statistical_mechanics.png/340px-Gibbs-Elementary_principles_in_statistical_mechanics.png 2x" data-file-width="918" data-file-height="1463" /></a><figcaption>Title page of Gibbs's <a href="/wiki/Elementary_Principles_in_Statistical_Mechanics" title="Elementary Principles in Statistical Mechanics">Elementary Principles in Statistical Mechanics</a>, one of the founding documents of that discipline, published in 1902</figcaption></figure> The first half of the 20th century saw the publication of two influential textbooks that soon came to be regarded as founding documents of <a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">chemical thermodynamics</a>, both of which used and extended Gibbs's work in that field: these were Thermodynamics and the Free Energy of Chemical Processes (1923), by <a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Gilbert N. Lewis</a> and <a href="/wiki/Merle_Randall" title="Merle Randall">Merle Randall</a>, and Modern Thermodynamics by the Methods of Willard Gibbs (1933), by <a href="/wiki/Edward_A._Guggenheim" title="Edward A. Guggenheim">Edward A. Guggenheim</a>.<a href="#cite_note-Ott-69">[69]</a> Gibbs's work on statistical ensembles, as presented in his 1902 textbook, has had a great impact in both theoretical physics and in pure mathematics.<a href="#cite_note-Wightman-77">[77]</a><a href="#cite_note-Wiener-78">[78]</a> According to mathematical physicist <a href="/wiki/Arthur_Wightman" title="Arthur Wightman">Arthur Wightman</a>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote">It is one of the striking features of the work of Gibbs, noticed by every student of thermodynamics and statistical mechanics, that his formulations of physical concepts were so felicitously chosen that they have survived 100 years of turbulent development in theoretical physics and mathematics.<div class="templatequotecite">— <cite>A. S. Wightman, 1990<a href="#cite_note-Wightman-77">[77]</a></cite></div></blockquote> Initially unaware of Gibbs's contributions in that field, <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> wrote three papers on statistical mechanics, published between 1902 and 1904. After reading Gibbs's textbook (which was translated into German by <a href="/wiki/Ernst_Zermelo" title="Ernst Zermelo">Ernst Zermelo</a> in 1905), Einstein declared that Gibbs's treatment was superior to his own and explained that he would not have written those papers if he had known Gibbs's work.<a href="#cite_note-Navarro-Einstein-102">[102]</a> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Wilson-2.jpg" class="mw-file-description"><img alt="Title page to a 1907 copy of Vector Analysis" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Wilson-2.jpg/150px-Wilson-2.jpg" decoding="async" width="150" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Wilson-2.jpg/225px-Wilson-2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Wilson-2.jpg/300px-Wilson-2.jpg 2x" data-file-width="3339" data-file-height="4719" /></a><figcaption>Title page to a 1907 copy of Vector Analysis</figcaption></figure> Gibbs's early papers on the use of graphical methods in thermodynamics reflect a powerfully original understanding of what mathematicians would later call "<a href="/wiki/Convex_analysis" title="Convex analysis">convex analysis</a>",<a href="#cite_note-103">[103]</a> including ideas that, according to <a href="/wiki/Barry_Simon" title="Barry Simon">Barry Simon</a>, "lay dormant for about seventy-five years".<a href="#cite_note-Simon-104">[104]</a> Important mathematical concepts based on Gibbs's work on thermodynamics and statistical mechanics include the <a href="/wiki/Gibbs_lemma" title="Gibbs lemma">Gibbs lemma</a> in <a href="/wiki/Game_theory" title="Game theory">game theory</a>, the <a href="/wiki/Gibbs%27_inequality" title="Gibbs' inequality">Gibbs inequality</a> in <a href="/wiki/Information_theory" title="Information theory">information theory</a>, as well as <a href="/wiki/Gibbs_sampling" title="Gibbs sampling">Gibbs sampling</a> in <a href="/wiki/Computational_statistics" title="Computational statistics">computational statistics</a>. The development of vector calculus was Gibbs's other great contribution to mathematics. The publication in 1901 of E. B. Wilson's textbook <a href="/wiki/Vector_Analysis" title="Vector Analysis">Vector Analysis</a>, based on Gibbs's lectures at Yale, did much to propagate the use of vectorial methods and notation in both mathematics and theoretical physics, definitively displacing the quaternions that had until then been dominant in the scientific literature.<a href="#cite_note-Marsden-105">[105]</a> At Yale, Gibbs was also mentor to Lee De Forest, who went on to invent the <a href="/wiki/Triode" title="Triode">triode</a> amplifier and has been called the "father of radio".<a href="#cite_note-Seeger-DeForest-106">[106]</a> De Forest credited Gibbs's influence for the realization "that the leaders in electrical development would be those who pursued the <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">higher theory of waves</a> and oscillations and the transmission by these means of intelligence and power."<a href="#cite_note-DeForest-55">[55]</a> Another student of Gibbs who played a significant role in the development of radio technology was Lynde Wheeler.<a href="#cite_note-107">[107]</a> Gibbs also had an indirect influence on mathematical economics. He supervised the thesis of <a href="/wiki/Irving_Fisher" title="Irving Fisher">Irving Fisher</a>, who received the first PhD in economics from Yale in 1891. In that work, published in 1892 as Mathematical Investigations in the Theory of Value and Prices, Fisher drew a direct analogy between Gibbsian equilibrium in physical and chemical systems, and the <a href="/wiki/General_equilibrium_theory" title="General equilibrium theory">general equilibrium</a> of markets, and he used Gibbs's vectorial notation.<a href="#cite_note-Fisher-53">[53]</a><a href="#cite_note-Celebrating-Fisher-54">[54]</a> Gibbs's protégé Edwin Bidwell Wilson became, in turn, a mentor to leading American economist and Nobel Laureate <a href="/wiki/Paul_Samuelson" title="Paul Samuelson">Paul Samuelson</a>.<a href="#cite_note-Samuelson-lecture-108">[108]</a> In 1947, Samuelson published <a href="/wiki/Foundations_of_Economic_Analysis" title="Foundations of Economic Analysis">Foundations of Economic Analysis</a>, based on his doctoral dissertation, in which he used as <a href="/wiki/Epigraph_(literature)" title="Epigraph (literature)">epigraph</a> a remark attributed to Gibbs: "Mathematics is a language." Samuelson later explained that in his understanding of prices his "debts were not primarily to <a href="/wiki/Vilfredo_Pareto" title="Vilfredo Pareto">Pareto</a> or <a href="/wiki/Eugen_Slutsky" title="Eugen Slutsky">Slutsky</a>, but to the great thermodynamicist, Willard Gibbs of Yale."<a href="#cite_note-109">[109]</a> Mathematician <a href="/wiki/Norbert_Wiener" title="Norbert Wiener">Norbert Wiener</a> cited Gibbs's use of probability in the formulation of statistical mechanics as "the first great revolution of twentieth century physics" and as a major influence on his conception of <a href="/wiki/Cybernetics" title="Cybernetics">cybernetics</a>. Wiener explained in the preface to his book <a href="/wiki/The_Human_Use_of_Human_Beings" title="The Human Use of Human Beings">The Human Use of Human Beings</a> that it was "devoted to the impact of the Gibbsian point of view on modern life, both through the substantive changes it has made to working science, and through the changes it has made indirectly in our attitude to life in general."<a href="#cite_note-110">[110]</a> <div class="mw-heading mw-heading2"><h2 id="Commemoration">Commemoration</h2>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=15" title="Edit section: Commemoration">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:JWGibbs-bronze.jpg" class="mw-file-description"><img alt="Photograph of bronze memorial tablet of Willard Gibbs" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/JWGibbs-bronze.jpg/170px-JWGibbs-bronze.jpg" decoding="async" width="170" height="221" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/JWGibbs-bronze.jpg/255px-JWGibbs-bronze.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/76/JWGibbs-bronze.jpg/340px-JWGibbs-bronze.jpg 2x" data-file-width="437" data-file-height="568" /></a><figcaption>Bronze memorial tablet, originally installed in 1912 at the Sloane Physics Laboratory, now at the entrance to the Josiah Willard Gibbs Laboratories, Yale University.</figcaption></figure> When the German physical chemist <a href="/wiki/Walther_Nernst" title="Walther Nernst">Walther Nernst</a> visited Yale in 1906 to give the <a href="/wiki/Silliman_Memorial_Lectures" title="Silliman Memorial Lectures">Silliman lecture</a>, he was surprised to find no tangible memorial for Gibbs. Nernst donated his $500 lecture fee to the university to help pay for a suitable monument. This was finally unveiled in 1912, in the form of a bronze bas-relief by sculptor <a href="/wiki/Lee_Lawrie" title="Lee Lawrie">Lee Lawrie</a>, installed in the Sloane Physics Laboratory.<a href="#cite_note-Seeger-memorial-111">[111]</a> In 1910, the <a href="/wiki/American_Chemical_Society" title="American Chemical Society">American Chemical Society</a> established the <a href="/wiki/Willard_Gibbs_Award" title="Willard Gibbs Award">Willard Gibbs Award</a> for eminent work in pure or applied chemistry.<a href="#cite_note-112">[112]</a> In 1923, the <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a> endowed the <a href="/wiki/Josiah_Willard_Gibbs_Lectureship" title="Josiah Willard Gibbs Lectureship">Josiah Willard Gibbs Lectureship</a>, "to show the public some idea of the aspects of mathematics and its applications".<a href="#cite_note-113">[113]</a> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:JWGibbsLabs.jpg" class="mw-file-description"><img alt="Photograph of the J. W. Gibbs Laboratories, Yale University" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/JWGibbsLabs.jpg/220px-JWGibbsLabs.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/JWGibbsLabs.jpg/330px-JWGibbsLabs.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/JWGibbsLabs.jpg/440px-JWGibbsLabs.jpg 2x" data-file-width="2560" data-file-height="1920" /></a><figcaption>Building housing the Josiah Willard Gibbs Laboratories, at Yale University's <a href="/wiki/Science_Hill_(Yale_University)" title="Science Hill (Yale University)">Science Hill</a></figcaption></figure> In 1945, Yale University created the J. Willard Gibbs Professorship in Theoretical Chemistry, held until 1973 by <a href="/wiki/Lars_Onsager" title="Lars Onsager">Lars Onsager</a>. Onsager, who much like Gibbs, focused on applying new mathematical ideas to problems in physical chemistry, won the 1968 Nobel Prize in chemistry.<a href="#cite_note-114">[114]</a> In addition to establishing the Josiah Willard Gibbs Laboratories and the J. Willard Gibbs Assistant Professorship in Mathematics, Yale has also hosted two symposia dedicated to Gibbs's life and work, one in 1989 and another on the centenary of his death, in 2003.<a href="#cite_note-115">[115]</a> <a href="/wiki/Rutgers_University" title="Rutgers University">Rutgers University</a> endowed a J. Willard Gibbs Professorship of Thermomechanics, held as of 2014 by Bernard Coleman.<a href="#cite_note-116">[116]</a> Gibbs was elected in 1950 to the <a href="/wiki/Hall_of_Fame_for_Great_Americans" title="Hall of Fame for Great Americans">Hall of Fame for Great Americans</a>.<a href="#cite_note-HallofFame-117">[117]</a> The <a href="/wiki/Oceanographic_research_ship" class="mw-redirect" title="Oceanographic research ship">oceanographic research ship</a> <a href="/wiki/USNS_Josiah_Willard_Gibbs_(T-AGOR-1)" class="mw-redirect" title="USNS Josiah Willard Gibbs (T-AGOR-1)">USNS Josiah Willard Gibbs (T-AGOR-1)</a> was in service with the <a href="/wiki/United_States_Navy" title="United States Navy">United States Navy</a> from 1958 to 1971.<a href="#cite_note-ship-118">[118]</a> <a href="/wiki/Gibbs_(crater)" title="Gibbs (crater)">Gibbs crater</a>, near the eastern <a href="/wiki/Lunar_limb" title="Lunar limb">limb</a> of the <a href="/wiki/Moon" title="Moon">Moon</a>, was named in the scientist's honor in 1964.<a href="#cite_note-119">[119]</a> <a href="/wiki/Edward_Guggenheim" class="mw-redirect" title="Edward Guggenheim">Edward Guggenheim</a> introduced the symbol G for the Gibbs free energy in 1933, and this was used also by <a href="/wiki/Dirk_ter_Haar" title="Dirk ter Haar">Dirk ter Haar</a> in 1966.<a href="#cite_note-G-120">[120]</a> This notation is now universal and is recommended by the <a href="/wiki/International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a>.<a href="#cite_note-IUPAC-G-121">[121]</a> In 1960, William Giauque and others suggested the name "gibbs" (abbreviated gbs.) for the unit of entropy <a href="/wiki/Calorie" title="Calorie">calorie</a> per <a href="/wiki/Kelvin" title="Kelvin">kelvin</a>,<a href="#cite_note-Giauque-unit-122">[122]</a> but this usage did not become common, and the corresponding <a href="/wiki/International_System_of_Units" title="International System of Units">SI</a> unit <a href="/wiki/Joule" title="Joule">joule</a> per kelvin carries no special name. In 1954, a year before his death, Albert Einstein was asked by an interviewer who were the greatest thinkers that he had known. Einstein replied: "<a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a>", adding "I never met Willard Gibbs; perhaps, had I done so, I might have placed him beside Lorentz."<a href="#cite_note-Pais-123">[123]</a> Author <a href="/wiki/Bill_Bryson" title="Bill Bryson">Bill Bryson</a> in his bestselling <a href="/wiki/Popular_science" title="Popular science">popular science</a> book <a href="/wiki/A_Short_History_of_Nearly_Everything" title="A Short History of Nearly Everything">A Short History of Nearly Everything</a> ranks Gibbs as "perhaps the most brilliant person that most people have never heard of".<a href="#cite_note-124">[124]</a> In 1958, USS San Carlos was renamed <a href="/wiki/USS_San_Carlos_(AVP-51)#Oceanographic_research_ship" class="mw-redirect" title="USS San Carlos (AVP-51)">USNS Josiah Willard Gibbs</a> and re-designated as an oceanographic research ship. <div class="mw-heading mw-heading3"><h3 id="In_literature">In literature</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=16" title="Edit section: In literature">edit</a>]</div> In 1909, the American historian and novelist <a href="/wiki/Henry_Adams" title="Henry Adams">Henry Adams</a> finished an essay entitled "The Rule of Phase Applied to History", in which he sought to apply Gibbs's phase rule and other thermodynamic concepts to a general theory of human history. <a href="/wiki/William_James" title="William James">William James</a>, Henry Bumstead, and others criticized both Adams's tenuous grasp of the scientific concepts that he invoked, as well as the arbitrariness of his application of those concepts as metaphors for the evolution of human thought and society.<a href="#cite_note-Mindel-Adams-125">[125]</a> The essay remained unpublished until it appeared posthumously in 1919, in The Degradation of the Democratic Dogma, edited by Henry Adams's younger brother <a href="/wiki/Brooks_Adams" title="Brooks Adams">Brooks</a>.<a href="#cite_note-Degradation-126">[126]</a> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Fortune_June_1946.jpg" class="mw-file-description"><img alt="Cover of June 1946 issue of Fortune magazine, showing an artist's rendition of Gibbs's thermodynamic surface for water" src="//upload.wikimedia.org/wikipedia/en/thumb/2/28/Fortune_June_1946.jpg/170px-Fortune_June_1946.jpg" decoding="async" width="170" height="216" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/2/28/Fortune_June_1946.jpg/255px-Fortune_June_1946.jpg 1.5x, //upload.wikimedia.org/wikipedia/en/2/28/Fortune_June_1946.jpg 2x" data-file-width="280" data-file-height="355" /></a><figcaption>Cover of the June 1946 issue of <a href="/wiki/Fortune_(magazine)" title="Fortune (magazine)">Fortune</a>, by artist Arthur Lidov, showing Gibbs's thermodynamic surface of water and his formula for the phase rule</figcaption></figure> In the 1930s, feminist poet <a href="/wiki/Muriel_Rukeyser" title="Muriel Rukeyser">Muriel Rukeyser</a> became fascinated by Willard Gibbs and wrote a long poem about his life and work ("Gibbs", included in the collection A Turning Wind, published in 1939), as well as a book-length biography (Willard Gibbs, 1942).<a href="#cite_note-Gander-Lives-127">[127]</a> According to Rukeyser: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote">Willard Gibbs is the type of the imagination at work in the world. His story is that of an opening up which has had its effect on our lives and our thinking; and, it seems to me, it is the emblem of the naked imagination—which is called abstract and impractical, but whose discoveries can be used by anyone who is interested, in whatever "field"—an imagination which for me, more than that of any other figure in American thought, any poet, or political, or religious figure, stands for imagination at its essential points.<div class="templatequotecite">— <cite>Muriel Rukeyser, 1949<a href="#cite_note-Rukeyser-PT-128">[128]</a></cite></div></blockquote> In 1946, <a href="/wiki/Fortune_(magazine)" title="Fortune (magazine)">Fortune</a> magazine illustrated a cover story on "Fundamental Science" with a representation of the <a href="/wiki/Maxwell%27s_thermodynamic_surface" title="Maxwell's thermodynamic surface">thermodynamic surface</a> that Maxwell had built based on Gibbs's proposal. Rukeyser called this surface a "statue of water"<a href="#cite_note-129">[129]</a> and the magazine saw in it "the abstract creation of a great American scientist that lends itself to the symbolism of contemporary art forms."<a href="#cite_note-Fortune-130">[130]</a> The artwork by Arthur Lidov also included Gibbs's mathematical expression of the phase rule for heterogeneous mixtures, as well as a <a href="/wiki/Radar" title="Radar">radar</a> screen, an <a href="/wiki/Oscilloscope" title="Oscilloscope">oscilloscope</a> waveform, <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton's</a> apple, and a small rendition of a three-dimensional phase diagram.<a href="#cite_note-Fortune-130">[130]</a> Gibbs's nephew, Ralph Gibbs Van Name, a professor of physical chemistry at Yale, was unhappy with Rukeyser's biography, in part because of her lack of scientific training. Van Name had withheld the family papers from her and, after her book was published in 1942 to positive literary but mixed scientific reviews, he tried to encourage Gibbs's former students to produce a more technically oriented biography.<a href="#cite_note-family-papers-131">[131]</a> Rukeyser's approach to Gibbs was also sharply criticized by Gibbs's former student and protégé Edwin Wilson.<a href="#cite_note-Wilson-rev1-132">[132]</a> With Van Name's and Wilson's encouragement, physicist Lynde Wheeler published a new biography of Gibbs in 1951.<a href="#cite_note-Wheeler-preface-133">[133]</a><a href="#cite_note-Wilson-rev2-134">[134]</a> Both Gibbs and Rukeyser's biography of him figure prominently in the poetry collection True North (1997) by <a href="/wiki/Stephanie_Strickland" title="Stephanie Strickland">Stephanie Strickland</a>.<a href="#cite_note-Strickland-135">[135]</a> In fiction, Gibbs appears as the mentor to character Kit Traverse in <a href="/wiki/Thomas_Pynchon" title="Thomas Pynchon">Thomas Pynchon</a>'s novel <a href="/wiki/Against_the_Day" title="Against the Day">Against the Day</a> (2006). That novel also prominently discusses the birefringence of <a href="/wiki/Iceland_spar" title="Iceland spar">Iceland spar</a>, an optical phenomenon that Gibbs investigated.<a href="#cite_note-Pynchon-136">[136]</a> <div class="mw-heading mw-heading3"><h3 id="Gibbs_stamp_(2005)">Gibbs stamp (2005)</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=17" title="Edit section: Gibbs stamp (2005)">edit</a>]</div> In 2005, the <a href="/wiki/United_States_Postal_Service" title="United States Postal Service">United States Postal Service</a> issued the American Scientists commemorative <a href="/wiki/Postage_stamp" title="Postage stamp">postage stamp</a> series designed by artist <a href="/wiki/Victor_Stabin" title="Victor Stabin">Victor Stabin</a>, depicting Gibbs, <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a>, <a href="/wiki/Barbara_McClintock" title="Barbara McClintock">Barbara McClintock</a>, and <a href="/wiki/Richard_Feynman" title="Richard Feynman">Richard Feynman</a>. The <a href="/wiki/First_day_of_issue" title="First day of issue">first day of issue</a> ceremony for the series was held on May 4 at Yale University's Luce Hall and was attended by <a href="/wiki/John_Marburger" title="John Marburger">John Marburger</a>, scientific advisor to the president of the United States, <a href="/wiki/Rick_Levin" title="Rick Levin">Rick Levin</a>, president of Yale, and family members of the scientists honored, including physician John W. Gibbs, a distant cousin of Willard Gibbs.<a href="#cite_note-stamp-issue-137">[137]</a> Kenneth R. Jolls, a professor of chemical engineering at <a href="/wiki/Iowa_State_University" title="Iowa State University">Iowa State University</a> and an expert on graphical methods in thermodynamics, consulted on the design of the stamp honoring Gibbs.<a href="#cite_note-Jolls-stamp-138">[138]</a><a href="#cite_note-ISU-stamp-139">[139]</a><a href="#cite_note-chem-eng-stamp-140">[140]</a> The stamp identifies Gibbs as a "thermodynamicist" and features a diagram from the 4th edition of Maxwell's Theory of Heat, published in 1875, which illustrates Gibbs's thermodynamic surface for water.<a href="#cite_note-ISU-stamp-139">[139]</a><a href="#cite_note-chem-eng-stamp-140">[140]</a> <a href="/wiki/Microprinting" title="Microprinting">Microprinting</a> on the <a href="/wiki/Collar_(clothing)" title="Collar (clothing)">collar</a> of Gibbs's portrait depicts his original mathematical equation for the change in the energy of a substance in terms of its entropy and the other state variables.<a href="#cite_note-Spakovszky-stamp-141">[141]</a> <div class="mw-heading mw-heading2"><h2 id="Outline_of_principal_work">Outline of principal work</h2>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=18" title="Edit section: Outline of principal work">edit</a>]</div> <ul><li><a href="/wiki/Physical_chemistry" title="Physical chemistry">Physical chemistry</a>: <a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">free energy</a>, <a href="/wiki/Phase_diagram" title="Phase diagram">phase diagram</a>, <a href="/wiki/Phase_rule" title="Phase rule">phase rule</a>, <a href="/wiki/Transport_phenomena" title="Transport phenomena">transport phenomena</a></li> <li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical mechanics</a>: <a href="/wiki/Statistical_ensemble_(mathematical_physics)" class="mw-redirect" title="Statistical ensemble (mathematical physics)">statistical ensemble</a>, <a href="/wiki/Phase_space" title="Phase space">phase space</a>, <a href="/wiki/Chemical_potential" title="Chemical potential">chemical potential</a>, <a href="/wiki/Gibbs_entropy" class="mw-redirect" title="Gibbs entropy">Gibbs entropy</a>, <a href="/wiki/Gibbs_paradox" title="Gibbs paradox">Gibbs paradox</a></li> <li><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a>: <a href="/wiki/Vector_Analysis_(Gibbs/Wilson)" class="mw-redirect" title="Vector Analysis (Gibbs/Wilson)">Vector Analysis</a>, <a href="/wiki/Convex_analysis" title="Convex analysis">convex analysis</a>, <a href="/wiki/Gibbs_phenomenon" title="Gibbs phenomenon">Gibbs phenomenon</a></li> <li><a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetism</a>: <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a>, <a href="/wiki/Birefringence" title="Birefringence">birefringence</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a 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Retrieved June 16, 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+MacTutor+History+of+Mathematics+archive&rft.atitle=Josiah+Willard+Gibbs&rft.date=1997&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=http%3A%2F%2Fwww-groups.dcs.st-and.ac.uk%2Fhistory%2FBiographies%2FGibbs.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Rukeyser-CTAcademy-10">^ <a href="#cite_ref-Rukeyser-CTAcademy_10-0">a</a> <a href="#cite_ref-Rukeyser-CTAcademy_10-1">b</a> Rukeyser 1988, p. 104 </li> <li id="cite_note-Wheeler-college-11">^ <a href="#cite_ref-Wheeler-college_11-0">a</a> <a href="#cite_ref-Wheeler-college_11-1">b</a> Wheeler 1998, pp. 23–24 </li> <li id="cite_note-Rukeyser-inheritance-12"><a href="#cite_ref-Rukeyser-inheritance_12-0">^</a> Rukeyser 1998, pp. 120, 142 </li> <li id="cite_note-Wheeler-astigmatism-13">^ <a href="#cite_ref-Wheeler-astigmatism_13-0">a</a> <a href="#cite_ref-Wheeler-astigmatism_13-1">b</a> Wheeler 1998, pp. 29–31 </li> <li id="cite_note-Rukeyser-astigmatism-14"><a href="#cite_ref-Rukeyser-astigmatism_14-0">^</a> Rukeyser 1988, p. 143 </li> <li id="cite_note-Wheeler-war-15"><a href="#cite_ref-Wheeler-war_15-0">^</a> Wheeler 1998, p. 30 </li> <li id="cite_note-Rukeyser-war-16"><a href="#cite_ref-Rukeyser-war_16-0">^</a> Rukeyser 1998, p. 134 </li> <li id="cite_note-17"><a href="#cite_ref-17">^</a> Wheeler 1998, p. 44 </li> <li id="cite_note-Wheeler-PhD-18">^ <a href="#cite_ref-Wheeler-PhD_18-0">a</a> <a href="#cite_ref-Wheeler-PhD_18-1">b</a> Wheeler 1998, p. 32 </li> <li id="cite_note-19"><a href="#cite_ref-19">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGibbs1863" class="citation book cs1">Gibbs, Josiah W. (1863). <a rel="nofollow" class="external text" href="http://brbl-dl.library.yale.edu/vufind/Record/3439123">On the form of the teeth of wheels in spur gearing</a>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1863PhDT.........1G">1863PhDT.........1G</a>. 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Retrieved December 28, 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Yale+Alumni+Magazine&rft.atitle=The+man+who+invented+radio&rft.volume=72&rft.issue=2&rft.date=2008-11&rft.aulast=Schiff&rft.aufirst=Judith&rft_id=http%3A%2F%2Fwww.yalealumnimagazine.com%2Farticles%2F2285&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-56"><a href="#cite_ref-56">^</a> Wheeler 1998, p. 197 </li> <li id="cite_note-57"><a href="#cite_ref-57">^</a> Wheeler 1998, pp. 197–199 </li> <li id="cite_note-Wheeler-portrait-58">^ <a href="#cite_ref-Wheeler-portrait_58-0">a</a> <a href="#cite_ref-Wheeler-portrait_58-1">b</a> Wheeler 1998, pp. 179–180. </li> <li id="cite_note-Seeger-gentleman-59">^ <a href="#cite_ref-Seeger-gentleman_59-0">a</a> <a href="#cite_ref-Seeger-gentleman_59-1">b</a> <a href="#cite_ref-Seeger-gentleman_59-2">c</a> <a href="#cite_ref-Seeger-gentleman_59-3">d</a> Seeger 1974, pp. 15–16. </li> <li id="cite_note-obituary-church-60"><a href="#cite_ref-obituary-church_60-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=rVkdAQAAIAAJ&pg=PA238">Obituary Record of Graduates of Yale University, 1901–1910</a>. 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A Historical Price Index for Use as a Deflator of Money Values in the Economy of the United States: Addenda et Corrigenda</a> (PDF). <a href="/wiki/American_Antiquarian_Society" title="American Antiquarian Society">American Antiquarian Society</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=How+Much+Is+That+in+Real+Money%3F+A+Historical+Price+Index+for+Use+as+a+Deflator+of+Money+Values+in+the+Economy+of+the+United+States%3A+Addenda+et+Corrigenda&rft.pub=American+Antiquarian+Society&rft.date=1997&rft.aulast=McCusker&rft.aufirst=J.+J.&rft_id=https%3A%2F%2Fwww.americanantiquarian.org%2Fproceedings%2F44525121.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> 1700–1799: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcCusker1992" class="citation book cs1"><a href="/wiki/John_J._McCusker" title="John J. McCusker">McCusker, J. 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A Historical Price Index for Use as a Deflator of Money Values in the Economy of the United States</a> (PDF). <a href="/wiki/American_Antiquarian_Society" title="American Antiquarian Society">American Antiquarian Society</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=How+Much+Is+That+in+Real+Money%3F+A+Historical+Price+Index+for+Use+as+a+Deflator+of+Money+Values+in+the+Economy+of+the+United+States&rft.pub=American+Antiquarian+Society&rft.date=1992&rft.aulast=McCusker&rft.aufirst=J.+J.&rft_id=https%3A%2F%2Fwww.americanantiquarian.org%2Fproceedings%2F44517778.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> 1800–present: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFederal_Reserve_Bank_of_Minneapolis" class="citation web cs1">Federal Reserve Bank of Minneapolis. <a rel="nofollow" class="external text" href="https://www.minneapolisfed.org/about-us/monetary-policy/inflation-calculator/consumer-price-index-1800-">"Consumer Price Index (estimate) 1800–"</a>. 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Chemical Thermodynamics – Principles and Applications. Academic Press. pp. 1, 213–214. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-530990-5" title="Special:BookSources/978-0-12-530990-5"><bdi>978-0-12-530990-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemical+Thermodynamics+%E2%80%93+Principles+and+Applications&rft.pages=1%2C+213-214&rft.pub=Academic+Press&rft.date=2000&rft.isbn=978-0-12-530990-5&rft.aulast=Ott&rft.aufirst=Bevan+J.&rft.au=Boerio-Goates%2C+Juliana&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-70"><a href="#cite_ref-70">^</a> Wheeler 1998, p. 79. </li> <li id="cite_note-Nolte2010-71">^ <a href="#cite_ref-Nolte2010_71-0">a</a> <a href="#cite_ref-Nolte2010_71-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNolte2010" class="citation journal cs1">Nolte, David D. (2010). "The tangled tale of phase space". Physics Today. 63 (4): 33–38. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010PhT....63d..33N">2010PhT....63d..33N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.3397041">10.1063/1.3397041</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:17205307">17205307</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=The+tangled+tale+of+phase+space&rft.volume=63&rft.issue=4&rft.pages=33-38&rft.date=2010&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A17205307%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1063%2F1.3397041&rft_id=info%3Abibcode%2F2010PhT....63d..33N&rft.aulast=Nolte&rft.aufirst=David+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-72"><a href="#cite_ref-72">^</a> For a mechanical system composed of n particles, the phase is represented by a point in a 2n-dimensional space, which he called "extension-in-phase" and is equivalent to our modern notion of phase space. However, the phrase "phase space" was not invented by him.<a href="#cite_note-Nolte2010-71">[71]</a> </li> <li id="cite_note-73"><a href="#cite_ref-73">^</a> Wheeler 1998, pp. 155–159. </li> <li id="cite_note-jaynes1965-74"><a href="#cite_ref-jaynes1965_74-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJaynes1965" class="citation journal cs1"><a href="/wiki/Edwin_Thompson_Jaynes" title="Edwin Thompson Jaynes">Jaynes, E. T.</a> (1965). "Gibbs vs Boltzmann Entropies". American Journal of Physics. 33 (5): 391–398. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1965AmJPh..33..391J">1965AmJPh..33..391J</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1971557">10.1119/1.1971557</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Gibbs+vs+Boltzmann+Entropies&rft.volume=33&rft.issue=5&rft.pages=391-398&rft.date=1965&rft_id=info%3Adoi%2F10.1119%2F1.1971557&rft_id=info%3Abibcode%2F1965AmJPh..33..391J&rft.aulast=Jaynes&rft.aufirst=E.+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Reif-75"><a href="#cite_ref-Reif_75-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrillouin1962" class="citation book cs1"><a href="/wiki/L%C3%A9on_Brillouin" title="Léon Brillouin">Brillouin, Léon</a> (1962). Science and information theory. Academic Press. pp. 119–124.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Science+and+information+theory&rft.pages=119-124&rft.pub=Academic+Press&rft.date=1962&rft.aulast=Brillouin&rft.aufirst=L%C3%A9on&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Poincare-76"><a href="#cite_ref-Poincare_76-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré1904" class="citation book cs1"><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré, Henri</a> (1904). <a class="external text" href="https://en.wikisource.org/wiki/The_Principles_of_Mathematical_Physics">"The Principles of Mathematical Physics" </a>. The Foundations of Science (The Value of Science). New York: Science Press. pp. 297–320.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Principles+of+Mathematical+Physics&rft.btitle=The+Foundations+of+Science+%28The+Value+of+Science%29&rft.place=New+York&rft.pages=297-320&rft.pub=Science+Press&rft.date=1904&rft.aulast=Poincar%C3%A9&rft.aufirst=Henri&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Wightman-77">^ <a href="#cite_ref-Wightman_77-0">a</a> <a href="#cite_ref-Wightman_77-1">b</a> <a href="#cite_ref-Wightman_77-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWightman1990" class="citation book cs1"><a href="/wiki/Arthur_Wightman" title="Arthur Wightman">Wightman, Arthur S.</a> (1990). "On the Prescience of J. Willard Gibbs". Proceedings of the Gibbs Symposium. pp. 23–38.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=On+the+Prescience+of+J.+Willard+Gibbs&rft.btitle=Proceedings+of+the+Gibbs+Symposium&rft.pages=23-38&rft.date=1990&rft.aulast=Wightman&rft.aufirst=Arthur+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Wiener-78">^ <a href="#cite_ref-Wiener_78-0">a</a> <a href="#cite_ref-Wiener_78-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWiener1961" class="citation book cs1">Wiener, Norbert (1961). "II: Groups and Statistical Mechanics". Cybernetics: or Control and Communication in the Animal and the Machine (2 ed.). MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-23007-0" title="Special:BookSources/978-0-262-23007-0"><bdi>978-0-262-23007-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=II%3A+Groups+and+Statistical+Mechanics&rft.btitle=Cybernetics%3A+or+Control+and+Communication+in+the+Animal+and+the+Machine&rft.edition=2&rft.pub=MIT+Press&rft.date=1961&rft.isbn=978-0-262-23007-0&rft.aulast=Wiener&rft.aufirst=Norbert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-79"><a href="#cite_ref-79">^</a> Wheeler 1998, pp. 160–161. </li> <li id="cite_note-80"><a href="#cite_ref-80">^</a> See, e.g., <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuang1987" class="citation book cs1"><a href="/wiki/Kerson_Huang" title="Kerson Huang">Huang, Kerson</a> (1987). Statistical Mechanics (2 ed.). John Wiley & Sons. pp. 140–143. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-81518-1" title="Special:BookSources/978-0-471-81518-1"><bdi>978-0-471-81518-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Statistical+Mechanics&rft.pages=140-143&rft.edition=2&rft.pub=John+Wiley+%26+Sons&rft.date=1987&rft.isbn=978-0-471-81518-1&rft.aulast=Huang&rft.aufirst=Kerson&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-81"><a href="#cite_ref-81">^</a> Wheeler 1998, pp. 107-108, 110 </li> <li id="cite_note-Grassmann-algebra-82"><a href="#cite_ref-Grassmann-algebra_82-0">^</a> Letter by Gibbs to <a href="/wiki/Victor_Schlegel" title="Victor Schlegel">Victor Schlegel</a>, quoted in Wheeler 1998, pp. 107–109 </li> <li id="cite_note-Grassmann-tides-83"><a href="#cite_ref-Grassmann-tides_83-0">^</a> Wheeler 1998, pp. 113–116 </li> <li id="cite_note-MacTutor_Grassmann-84"><a href="#cite_ref-MacTutor_Grassmann_84-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson2005" class="citation web cs1">O'Connor, John J.; Robertson, Edmund F. (2005). <a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Grassmann.html">"Hermann Günter Grassmann"</a>. The MacTutor History of Mathematics archive. University of St Andrews, Scotland. School of Mathematics and Statistics.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+MacTutor+History+of+Mathematics+archive&rft.atitle=Hermann+G%C3%BCnter+Grassmann&rft.date=2005&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=http%3A%2F%2Fwww-history.mcs.st-andrews.ac.uk%2FBiographies%2FGrassmann.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Crowe1967-85"><a href="#cite_ref-Crowe1967_85-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMichael_J._Crowe1967" class="citation book cs1"><a href="/wiki/Michael_J._Crowe" title="Michael J. Crowe">Michael J. Crowe</a> (1967). A History of Vector Analysis: The Evolution of the Idea of a Vectorial System. Courier Corporation. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-67910-5" title="Special:BookSources/978-0-486-67910-5"><bdi>978-0-486-67910-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Vector+Analysis%3A+The+Evolution+of+the+Idea+of+a+Vectorial+System&rft.pub=Courier+Corporation&rft.date=1967&rft.isbn=978-0-486-67910-5&rft.au=Michael+J.+Crowe&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-86"><a href="#cite_ref-86">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShmueli2006" class="citation book cs1">Shmueli, Uri (2006). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131104024615/http://www.mendeley.com/research/11-reciprocal-space-crystallography/#page-1">"Reciprocal Space in Crystallography"</a>. International Tables for Crystallography. Vol. B. pp. 2–9. Archived from <a rel="nofollow" class="external text" href="http://www.mendeley.com/research/11-reciprocal-space-crystallography/#page-1">the original</a> on November 4, 2013. Retrieved February 25, 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Reciprocal+Space+in+Crystallography&rft.btitle=International+Tables+for+Crystallography&rft.pages=2-9&rft.date=2006&rft.aulast=Shmueli&rft.aufirst=Uri&rft_id=http%3A%2F%2Fwww.mendeley.com%2Fresearch%2F11-reciprocal-space-crystallography%2F%23page-1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Optics-87">^ <a href="#cite_ref-Optics_87-0">a</a> <a href="#cite_ref-Optics_87-1">b</a> Wheeler 1998, ch. 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University of Chicago Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-07887-8" title="Special:BookSources/978-0-226-07887-8"><bdi>978-0-226-07887-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Creation+of+Scientific+Effects%3A+Heinrich+Hertz+and+Electric+Waves&rft.pub=University+of+Chicago+Press&rft.date=1994&rft.isbn=978-0-226-07887-8&rft.aulast=Buchwald&rft.aufirst=Jed+Z.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Rukeyser-printing-89"><a href="#cite_ref-Rukeyser-printing_89-0">^</a> Rukeyser 1998, pp. 225–226 </li> <li id="cite_note-90"><a href="#cite_ref-90">^</a> Wightman 1979, pp. xiii, lxxx </li> <li id="cite_note-91"><a href="#cite_ref-91">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMüller2007" class="citation book cs1">Müller, Ingo (2007). A History of Thermodynamics – the Doctrine of Energy and Entropy. 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June 2, 1902. p. 9.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Times&rft.atitle=University+intelligence&rft.issue=36783&rft.pages=p.-9&rft.date=1902-06-02&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-94"><a href="#cite_ref-94">^</a> Rukeyser 1998, p. 345 </li> <li id="cite_note-Rota-95"><a href="#cite_ref-Rota_95-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRota1996" class="citation book cs1"><a href="/wiki/Gian-Carlo_Rota" title="Gian-Carlo Rota">Rota, Gian-Carlo</a> (1996). <a rel="nofollow" class="external text" href="https://archive.org/details/indiscretethough0000rota">Indiscrete Thoughts</a>. 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Archived from <a rel="nofollow" class="external text" href="http://www.history.navy.mil/danfs/s4/san_carlos.htm">the original</a> on July 12, 2011. Retrieved June 16, 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Dictionary+of+American+Naval+Fighting+Ships&rft.atitle=San+Carlos&rft_id=http%3A%2F%2Fwww.history.navy.mil%2Fdanfs%2Fs4%2Fsan_carlos.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-119"><a href="#cite_ref-119">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20171222162448/https://planetarynames.wr.usgs.gov/Feature/2155">"Gibbs"</a>. Gazetteer of Planetary Nomenclature. International Astronomical Union. Archived from <a rel="nofollow" class="external text" href="https://planetarynames.wr.usgs.gov/Feature/2155">the original</a> on December 22, 2017. Retrieved December 11, 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Gazetteer+of+Planetary+Nomenclature&rft.atitle=Gibbs&rft_id=http%3A%2F%2Fplanetarynames.wr.usgs.gov%2FFeature%2F2155&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-G-120"><a href="#cite_ref-G_120-0">^</a> Seeger 1974, p. 96 </li> <li id="cite_note-IUPAC-G-121"><a href="#cite_ref-IUPAC-G_121-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">"Gibbs energy (function), G". IUPAC Compendium of Chemical Terminology. 2009. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.G02629">10.1351/goldbook.G02629</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-9678550-9-7" title="Special:BookSources/978-0-9678550-9-7"><bdi>978-0-9678550-9-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Gibbs+energy+%28function%29%2C+G&rft.btitle=IUPAC+Compendium+of+Chemical+Terminology&rft.date=2009&rft_id=info%3Adoi%2F10.1351%2Fgoldbook.G02629&rft.isbn=978-0-9678550-9-7&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Giauque-unit-122"><a href="#cite_ref-Giauque-unit_122-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGiauqueHornungKunzlerRubin1960" class="citation journal cs1">Giauque, W. F.; Hornung, E. W.; Kunzler, J. E.; Rubin, T. R. (1960). "The Thermodynamic Properties of Aqueous Sulfuric Acid Solutions and Hydrates from 15 to 300K.1". Journal of the American Chemical Society. 82 (1): 62–70. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1960JAChS..82...62G">1960JAChS..82...62G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fja01486a014">10.1021/ja01486a014</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+American+Chemical+Society&rft.atitle=The+Thermodynamic+Properties+of+Aqueous+Sulfuric+Acid+Solutions+and+Hydrates+from+15+to+300K.1&rft.volume=82&rft.issue=1&rft.pages=62-70&rft.date=1960&rft_id=info%3Adoi%2F10.1021%2Fja01486a014&rft_id=info%3Abibcode%2F1960JAChS..82...62G&rft.aulast=Giauque&rft.aufirst=W.+F.&rft.au=Hornung%2C+E.+W.&rft.au=Kunzler%2C+J.+E.&rft.au=Rubin%2C+T.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Pais-123"><a href="#cite_ref-Pais_123-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPais1982" class="citation book cs1"><a href="/wiki/Abraham_Pais" title="Abraham Pais">Pais, Abraham</a> (1982). <a rel="nofollow" class="external text" href="https://archive.org/details/subtleislordscie00pais">Subtle is the Lord</a>. Oxford: Oxford University Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/subtleislordscie00pais/page/73">73</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-280672-7" title="Special:BookSources/978-0-19-280672-7"><bdi>978-0-19-280672-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Subtle+is+the+Lord&rft.place=Oxford&rft.pages=73&rft.pub=Oxford+University+Press&rft.date=1982&rft.isbn=978-0-19-280672-7&rft.aulast=Pais&rft.aufirst=Abraham&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsubtleislordscie00pais&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-124"><a href="#cite_ref-124">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBryson2003" class="citation book cs1">Bryson, Bill (2003). A Short History of Nearly Everything (1st paperback ed.). New York City: Broadway Books, Random House, Inc. p. 116. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7679-0818-X" title="Special:BookSources/0-7679-0818-X"><bdi>0-7679-0818-X</bdi></a>. <q>Gibbs is perhaps the most brilliant person that most people have never heard of. Modest to the point of near invisibility, he passed virtually the whole of his life, apart from three years spent studying in Europe, within a three-block area bounded by his house and the Yale campus in New Haven, Connecticut. For his first ten years at Yale he didn't even bother to draw a salary. (He had independent means.) From 1871, when he joined the university as a professor, to his death in 1903, his courses attracted an average of slightly over one student a semester. His written work was difficult to follow and employed a private form of notation that many found incomprehensible. But buried among his arcane formulations were insights of the loftiest brilliance.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Short+History+of+Nearly+Everything&rft.place=New+York+City&rft.pages=116&rft.edition=1st+paperback&rft.pub=Broadway+Books%2C+Random+House%2C+Inc.&rft.date=2003&rft.isbn=0-7679-0818-X&rft.aulast=Bryson&rft.aufirst=Bill&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Mindel-Adams-125"><a href="#cite_ref-Mindel-Adams_125-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMindel1965" class="citation journal cs1">Mindel, Joseph (1965). "The Uses of Metaphor: Henry Adams and the Symbols of Science". Journal of the History of Ideas. 26 (1): 89–102. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2708401">10.2307/2708401</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2708401">2708401</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+History+of+Ideas&rft.atitle=The+Uses+of+Metaphor%3A+Henry+Adams+and+the+Symbols+of+Science&rft.volume=26&rft.issue=1&rft.pages=89-102&rft.date=1965&rft_id=info%3Adoi%2F10.2307%2F2708401&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2708401%23id-name%3DJSTOR&rft.aulast=Mindel&rft.aufirst=Joseph&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Degradation-126"><a href="#cite_ref-Degradation_126-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAdams1919" class="citation book cs1"><a href="/wiki/Henry_Adams" title="Henry Adams">Adams, Henry</a> (1919). Adams, Brooks (ed.). <a rel="nofollow" class="external text" href="https://archive.org/details/thedegradationof00adamuoft">The Degradation of the Democratic Dogma</a>. New York: Macmillan. Retrieved May 5, 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Degradation+of+the+Democratic+Dogma&rft.place=New+York&rft.pub=Macmillan&rft.date=1919&rft.aulast=Adams&rft.aufirst=Henry&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fthedegradationof00adamuoft&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Gander-Lives-127"><a href="#cite_ref-Gander-Lives_127-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGander2013" class="citation book cs1">Gander, Catherine (2013). <a rel="nofollow" class="external text" href="https://archive.org/details/murielrukeyserdo0000unse/page/73/mode/2up">"The Lives"</a>. Muriel Rukeyser and Documentary: The Poetics of Connection. Edinburgh: Edinburgh University Press. pp. 73–120. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7486-7053-6" title="Special:BookSources/978-0-7486-7053-6"><bdi>978-0-7486-7053-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Lives&rft.btitle=Muriel+Rukeyser+and+Documentary%3A+The+Poetics+of+Connection&rft.place=Edinburgh&rft.pages=73-120&rft.pub=Edinburgh+University+Press&rft.date=2013&rft.isbn=978-0-7486-7053-6&rft.aulast=Gander&rft.aufirst=Catherine&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmurielrukeyserdo0000unse%2Fpage%2F73%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Rukeyser-PT-128"><a href="#cite_ref-Rukeyser-PT_128-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRukeyser1949" class="citation journal cs1">Rukeyser, Muriel (1949). "Josiah Willard Gibbs". Physics Today. 2 (2): 6–27. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1949PhT.....2b...6R">1949PhT.....2b...6R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.3066422">10.1063/1.3066422</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=Josiah+Willard+Gibbs&rft.volume=2&rft.issue=2&rft.pages=6-27&rft.date=1949&rft_id=info%3Adoi%2F10.1063%2F1.3066422&rft_id=info%3Abibcode%2F1949PhT.....2b...6R&rft.aulast=Rukeyser&rft.aufirst=Muriel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-129"><a href="#cite_ref-129">^</a> Rukeyser 1988, p. 203 </li> <li id="cite_note-Fortune-130">^ <a href="#cite_ref-Fortune_130-0">a</a> <a href="#cite_ref-Fortune_130-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1">"The Great Science Debate". <a href="/wiki/Fortune_(magazine)" title="Fortune (magazine)">Fortune</a>. 33 (6): 117. 1946.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Fortune&rft.atitle=The+Great+Science+Debate&rft.volume=33&rft.issue=6&rft.pages=117&rft.date=1946&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-family-papers-131"><a href="#cite_ref-family-papers_131-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoleman1986" class="citation web cs1">Holeman, Heather L. (1986). <a rel="nofollow" class="external text" href="http://drs.library.yale.edu/HLTransformer/HLTransServlet?stylename=yul.ead2002.xhtml.xsl&pid=beinecke:gibbs&query=&clear-stylesheet-cache=yes&hlon=yes&big=&adv=&filter=&hitPageStart=&sortFields=&view=all">"Guide to the Gibbs-Van Name Papers"</a>. Yale University Library. Retrieved January 18, 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Guide+to+the+Gibbs-Van+Name+Papers&rft.pub=Yale+University+Library&rft.date=1986&rft.aulast=Holeman&rft.aufirst=Heather+L.&rft_id=http%3A%2F%2Fdrs.library.yale.edu%2FHLTransformer%2FHLTransServlet%3Fstylename%3Dyul.ead2002.xhtml.xsl%26pid%3Dbeinecke%3Agibbs%26query%3D%26clear-stylesheet-cache%3Dyes%26hlon%3Dyes%26big%3D%26adv%3D%26filter%3D%26hitPageStart%3D%26sortFields%3D%26view%3Dall&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Wilson-rev1-132"><a href="#cite_ref-Wilson-rev1_132-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMiller1944" class="citation journal cs1">Miller, G. A. (1944). "Starring Subjects in "american Men of Science"". Science. 99 (2576): 386. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1944Sci....99..386M">1944Sci....99..386M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.99.2576.386">10.1126/science.99.2576.386</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17844056">17844056</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Starring+Subjects+in+%22american+Men+of+Science%22&rft.volume=99&rft.issue=2576&rft.pages=386&rft.date=1944&rft_id=info%3Apmid%2F17844056&rft_id=info%3Adoi%2F10.1126%2Fscience.99.2576.386&rft_id=info%3Abibcode%2F1944Sci....99..386M&rft.aulast=Miller&rft.aufirst=G.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Wheeler-preface-133"><a href="#cite_ref-Wheeler-preface_133-0">^</a> Wheeler 1998, pp. ix–xiii </li> <li id="cite_note-Wilson-rev2-134"><a href="#cite_ref-Wilson-rev2_134-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilson1951" class="citation journal cs1">Wilson, Edwin B. 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American Scientist. 39 (2): 287–289. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/27826371">27826371</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Scientist&rft.atitle=Josiah+Willard+Gibbs&rft.volume=39&rft.issue=2&rft.pages=287-289&rft.date=1951&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F27826371%23id-name%3DJSTOR&rft.aulast=Wilson&rft.aufirst=Edwin+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Strickland-135"><a href="#cite_ref-Strickland_135-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStrickland1997" class="citation book cs1"><a href="/wiki/Stephanie_Strickland" title="Stephanie Strickland">Strickland, Stephanie</a> (1997). True North. 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New York: Penguin. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-59420-120-2" title="Special:BookSources/978-1-59420-120-2"><bdi>978-1-59420-120-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Against+the+Day&rft.place=New+York&rft.pub=Penguin&rft.date=2006&rft.isbn=978-1-59420-120-2&rft.aulast=Pynchon&rft.aufirst=Thomas&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fagainstday00pync&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-stamp-issue-137"><a href="#cite_ref-stamp-issue_137-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20141030122112/http://www.yale.edu/opa/arc-ybc/v33.n29/story3.html">"Yale scientist featured in new stamp series"</a>. Yale Bulletin & Calendar. Vol. 33, no. 28. May 20, 2005. Archived from <a rel="nofollow" class="external text" href="http://www.yale.edu/opa/arc-ybc/v33.n29/story3.html">the original</a> on October 30, 2014. Retrieved November 30, 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Yale+Bulletin+%26+Calendar&rft.atitle=Yale+scientist+featured+in+new+stamp+series&rft.volume=33&rft.issue=28&rft.date=2005-05-20&rft_id=http%3A%2F%2Fwww.yale.edu%2Fopa%2Farc-ybc%2Fv33.n29%2Fstory3.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Jolls-stamp-138"><a href="#cite_ref-Jolls-stamp_138-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20121030193200/http://www.eng.iastate.edu/coe/feature/jolls.asp">"Iowa State Chemical Engineer Drives Issue of New Stamp Honoring Father of Thermodynamics"</a>. College Feature, Iowa State University, College of Engineering. 2004. Archived from <a rel="nofollow" class="external text" href="http://www.eng.iastate.edu/coe/feature/jolls.asp">the original</a> on October 30, 2012. Retrieved November 17, 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=College+Feature%2C+Iowa+State+University%2C+College+of+Engineering&rft.atitle=Iowa+State+Chemical+Engineer+Drives+Issue+of+New+Stamp+Honoring+Father+of+Thermodynamics&rft.date=2004&rft_id=http%3A%2F%2Fwww.eng.iastate.edu%2Fcoe%2Ffeature%2Fjolls.asp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-ISU-stamp-139">^ <a href="#cite_ref-ISU-stamp_139-0">a</a> <a href="#cite_ref-ISU-stamp_139-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHacker2004" class="citation news cs1">Hacker, Annette (November 11, 2004). <a rel="nofollow" class="external text" href="http://www.public.iastate.edu/~nscentral/news/04/nov/stamp.shtml">"ISU professor helps develop postage stamp honoring noted scientist"</a>. News Service, Iowa State University. Retrieved November 17, 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=News+Service%2C+Iowa+State+University&rft.atitle=ISU+professor+helps+develop+postage+stamp+honoring+noted+scientist&rft.date=2004-11-11&rft.aulast=Hacker&rft.aufirst=Annette&rft_id=http%3A%2F%2Fwww.public.iastate.edu%2F~nscentral%2Fnews%2F04%2Fnov%2Fstamp.shtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-chem-eng-stamp-140">^ <a href="#cite_ref-chem-eng-stamp_140-0">a</a> <a href="#cite_ref-chem-eng-stamp_140-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1">"Postal Service Pays Homage to Josiah Willard Gibbs". Chemical Engineering Progress. 101 (7): 57. 2005.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Chemical+Engineering+Progress&rft.atitle=Postal+Service+Pays+Homage+to+Josiah+Willard+Gibbs&rft.volume=101&rft.issue=7&rft.pages=57&rft.date=2005&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> <li id="cite_note-Spakovszky-stamp-141"><a href="#cite_ref-Spakovszky-stamp_141-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSpakovszky2005" class="citation journal cs1">Spakovszky, Zoltan (2005). <a rel="nofollow" class="external text" href="http://web.mit.edu/16.unified/www/FALL/thermodynamics/figures/MechEng-4-2006-Gibbs.pdf">"Stamp of Authenticity"</a> (PDF). Mechanical Engineering. 128 (4). ASME: 7. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/http://web.mit.edu/16.unified/www/FALL/thermodynamics/figures/MechEng-4-2006-Gibbs.pdf">Archived</a> (PDF) from the original on October 9, 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mechanical+Engineering&rft.atitle=Stamp+of+Authenticity&rft.volume=128&rft.issue=4&rft.pages=7&rft.date=2005&rft.aulast=Spakovszky&rft.aufirst=Zoltan&rft_id=http%3A%2F%2Fweb.mit.edu%2F16.unified%2Fwww%2FFALL%2Fthermodynamics%2Ffigures%2FMechEng-4-2006-Gibbs.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Bibliography">Bibliography</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=21" title="Edit section: Bibliography">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Primary">Primary</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=22" title="Edit section: Primary">edit</a>]</div> <ul><li>L. P. Wheeler, E. O. Waters and S. W. Dudley (eds.),The Early Work of Willard Gibbs in Applied Mechanics, (New York: Henry Schuman, 1947). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-881987-17-5" title="Special:BookSources/1-881987-17-5">1-881987-17-5</a>. This contains previously unpublished work by Gibbs, from the period between 1863 and 1871.</li> <li>J. W. Gibbs, "<a href="/wiki/On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of Heterogeneous Substances</a>", Transactions of the Connecticut Academy of Arts and Sciences, 3, 108–248, 343–524, (1874–1878). Reproduced in both The Scientific Papers (1906), <a rel="nofollow" class="external text" href="https://archive.org/stream/scientificpapers01gibbuoft#page/54/mode/2up">pp. 55–353</a> and The Collected Works of J. Willard Gibbs (1928), pp. 55–353.</li> <li><a href="/wiki/Edwin_Bidwell_Wilson" title="Edwin Bidwell Wilson">E. B. Wilson</a>, <a href="/wiki/Vector_Analysis" title="Vector Analysis">Vector Analysis, a text-book for the use of students of Mathematics and Physics, founded upon the Lectures of J. Willard Gibbs</a>, (New Haven: Yale University Press, 1929 [1901]).</li> <li>J. W. Gibbs, <a href="/wiki/Elementary_Principles_in_Statistical_Mechanics" title="Elementary Principles in Statistical Mechanics">Elementary Principles in Statistical Mechanics, developed with especial reference to the rational foundation of thermodynamics</a>, (New York: Dover Publications, 1960 [1902]).</li></ul> Gibbs's other papers are included in both: <ul><li>The Scientific Papers of J. Willard Gibbs, in two volumes, eds. H. A. Bumstead and R. G. Van Name, (Woodbridge, CT: Ox Bow Press, 1993 [1906]). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-918024-77-3" title="Special:BookSources/0-918024-77-3">0-918024-77-3</a>, <a href="/wiki/Special:BookSources/1-881987-06-X" title="Special:BookSources/1-881987-06-X">1-881987-06-X</a>. For scans of the 1906 printing, see <a rel="nofollow" class="external text" href="https://archive.org/stream/scientificpapers01gibbuoft#page/n5/mode/2up">vol. I</a> and <a rel="nofollow" class="external text" href="https://archive.org/stream/scientificpapers02gibbuoft#page/n3/mode/2up">vol. II</a>.</li> <li> The Collected Works of J. Willard Gibbs, in two volumes, eds. W. R. Longley and R. G. Van Name, (New Haven: Yale University Press, 1957 [1928]). For scans of the 1928 printing, see <a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k95192s">vol. I</a> and <a rel="nofollow" class="external text" href="https://archive.org/details/collectedworksj00longgoog">vol. II</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Secondary">Secondary</h3>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=23" title="Edit section: Secondary">edit</a>]</div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBumstead1903" class="citation journal cs1 cs1-prop-long-vol"><a href="/wiki/Henry_Andrews_Bumstead" class="mw-redirect" title="Henry Andrews Bumstead">Bumstead, H. A.</a> (1903). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1450126">"Josiah Willard Gibbs"</a>. American Journal of Science. s4-16 (93): 187–202. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1903AmJS...16..187A">1903AmJS...16..187A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2475%2Fajs.s4-16.93.187">10.2475/ajs.s4-16.93.187</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Science&rft.atitle=Josiah+Willard+Gibbs&rft.volume=s4-16&rft.issue=93&rft.pages=187-202&rft.date=1903&rft_id=info%3Adoi%2F10.2475%2Fajs.s4-16.93.187&rft_id=info%3Abibcode%2F1903AmJS...16..187A&rft.aulast=Bumstead&rft.aufirst=H.+A.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1450126&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988">. Reprinted with some additions in both The Scientific Papers, vol. I, <a rel="nofollow" class="external text" href="https://archive.org/stream/scientificpapers01gibbuoft#page/n15/mode/2up">pp. xiii–xxviiii</a> (1906) and The Collected Works of J. Willard Gibbs, vol. I, pp. xiii–xxviiii (1928). Also available here <a rel="nofollow" class="external autonumber" href="http://histmath-heidelberg.de/htmg/gibbs-bumstead.htm">[1]</a>.</li> <li>D. G. Caldi and G. D. Mostow (eds.), Proceedings of the Gibbs Symposium, Yale University, May 15–17, 1989, (American Mathematical Society and American Institute of Physics, 1990).</li> <li>W. H. Cropper, "The Greatest Simplicity: Willard Gibbs", in Great Physicists, (Oxford: Oxford University Press, 2001), pp. 106–123. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-517324-4" title="Special:BookSources/0-19-517324-4">0-19-517324-4</a></li> <li>M. J. Crowe, <a href="/wiki/A_History_of_Vector_Analysis" title="A History of Vector Analysis">A History of Vector Analysis: The Evolution of the Idea of a Vectorial System</a>, (New York: Dover, 1994 [1967]). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-67910-1" title="Special:BookSources/0-486-67910-1">0-486-67910-1</a></li> <li>J. G. Crowther, Famous American Men of Science, (Freeport, NY: Books for Libraries Press, 1969 [1937]). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8369-0040-5" title="Special:BookSources/0-8369-0040-5">0-8369-0040-5</a></li> <li>F. G. Donnan and A. E. Hass (eds.), A Commentary on the Scientific Writings of J. Willard Gibbs, in two volumes, (New York: Arno, 1980 [1936]). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-405-12544-5" title="Special:BookSources/0-405-12544-5">0-405-12544-5</a>. Only <a rel="nofollow" class="external text" href="https://archive.org/details/commentaryonscie01donn">vol I.</a> is currently available online.</li> <li><a href="/wiki/Pierre_Duhem" title="Pierre Duhem">P. Duhem</a>, <a rel="nofollow" class="external text" href="https://archive.org/details/josiahwillardgib00duheuoft">Josiah-Willard Gibbs à propos de la publication de ses Mémoires scientifiques</a>, (Paris: A. Herman, 1908).</li> <li>C. S. Hastings, <a rel="nofollow" class="external text" href="https://archive.org/stream/biographicalmemo011929mbp#page/n417/mode/2up">"Josiah Willard Gibbs"</a>, Biographical Memoirs of the National Academy of Sciences, 6, 373–393 (1909).</li> <li><a href="/wiki/Martin_J._Klein" title="Martin J. Klein">M. J. Klein</a>, "Gibbs, Josiah Willard", in Complete Dictionary of Scientific Biography, vol. 5, (Detroit: Charles Scribner's Sons, 2008), pp. 386–393.</li> <li><a href="/wiki/Muriel_Rukeyser" title="Muriel Rukeyser">M. Rukeyser</a>, Willard Gibbs: American Genius, (Woodbridge, CT: Ox Bow Press, 1988 [1942]). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-918024-57-9" title="Special:BookSources/0-918024-57-9">0-918024-57-9</a></li> <li><a href="/wiki/Raymond_Seeger" title="Raymond Seeger">R. J. Seeger</a>, J. Willard Gibbs, American mathematical physicist par excellence, (Oxford and New York: Pergamon Press, 1974). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-08-018013-2" title="Special:BookSources/0-08-018013-2">0-08-018013-2</a></li> <li><a href="/wiki/Lynde_Wheeler" title="Lynde Wheeler">L. P. Wheeler</a>, Josiah Willard Gibbs, The History of a Great Mind, (Woodbridge, CT: Ox Bow Press, 1998 [1951]). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-881987-11-6" title="Special:BookSources/1-881987-11-6">1-881987-11-6</a></li> <li><a href="/wiki/Arthur_Wightman" title="Arthur Wightman">A. S. Wightman</a>, "Convexity and the notion of equilibrium state in thermodynamics and statistical mechanics". Published as an introduction to R. B. Israel, Convexity in the Theory of Lattice Gases, (Princeton, NJ: Princeton University Press, 1979), pp. ix–lxxxv. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-08209-X" title="Special:BookSources/0-691-08209-X">0-691-08209-X</a></li> <li><a href="/wiki/Edwin_Bidwell_Wilson" title="Edwin Bidwell Wilson">E. B. Wilson</a>, <a rel="nofollow" class="external text" href="http://projecteuclid.org/euclid.bams/1183494779">"Reminiscences of Gibbs by a student and colleague"</a>, Bulletin of the American Mathematical Society, 37, 401–416 (1931).</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=Josiah_Willard_Gibbs&action=edit&section=24" title="Edit section: External links">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1250146164">.mw-parser-output .sister-box .side-box-abovebelow{padding:0.75em 0;text-align:center}.mw-parser-output .sister-box .side-box-abovebelow>b{display:block}.mw-parser-output .sister-box .side-box-text>ul{border-top:1px solid #aaa;padding:0.75em 0;width:217px;margin:0 auto}.mw-parser-output .sister-box .side-box-text>ul>li{min-height:31px}.mw-parser-output .sister-logo{display:inline-block;width:31px;line-height:31px;vertical-align:middle;text-align:center}.mw-parser-output .sister-link{display:inline-block;margin-left:4px;width:182px;vertical-align:middle}@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-v2.svg"]{background-color:white}}</style><div role="navigation" aria-labelledby="sister-projects" class="side-box metadata side-box-right sister-box sistersitebox plainlinks"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-abovebelow"> Josiah Willard Gibbs at Wikipedia's <a href="/wiki/Wikipedia:Wikimedia_sister_projects" title="Wikipedia:Wikimedia sister projects">sister projects</a></div> <div class="side-box-flex"> <div class="side-box-text plainlist"><ul><li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="20" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /><a href="https://commons.wikimedia.org/wiki/Josiah_Willard_Gibbs" class="extiw" title="c:Josiah Willard Gibbs">Media</a> from Commons</li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/23px-Wikiquote-logo.svg.png" decoding="async" width="23" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/35px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/46px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /><a href="https://en.wikiquote.org/wiki/Josiah_Willard_Gibbs" class="extiw" title="q:Josiah Willard Gibbs">Quotations</a> from Wikiquote</li><li><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/26px-Wikisource-logo.svg.png" decoding="async" width="26" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/39px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/51px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /><a href="https://en.wikisource.org/wiki/Author:Josiah_Willard_Gibbs" class="extiw" title="s:Author:Josiah Willard Gibbs">Texts</a> from Wikisource</li></ul></div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Gibbs.html">"Josiah Willard Gibbs"</a>, <a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Josiah+Willard+Gibbs&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FGibbs.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJosiah+Willard+Gibbs" class="Z3988"></li> <li>"<a rel="nofollow" class="external text" href="http://www.aip.org/history/gap/Gibbs/Gibbs.html">Josiah Willard Gibbs</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150501105303/http://www.aip.org/history/gap/Gibbs/Gibbs.html">Archived</a> May 1, 2015, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>", in Selected Papers of Great American Scientists, American Institute of Physics, (2003 [1976])</li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=132578">Josiah Willard Gibbs</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20131228162217/http://murielrukeyser.emuenglish.org/writing/gibbs/">"Gibbs"</a> by <a href="/wiki/Muriel_Rukeyser" title="Muriel Rukeyser">Muriel Rukeyser</a></li> <li><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1403.2460">Reflections on Gibbs: From Statistical Physics to the Amistad</a> by <a href="/wiki/Leo_Kadanoff" title="Leo Kadanoff">Leo Kadanoff</a>, Prof.</li> <li><a rel="nofollow" class="external text" href="http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/gibbs-josiah.pdf">National Academy of Sciences, Biography, Josiah Willard Gibbs</a></li> <li><a href="https://hdl.handle.net/10079/fa/beinecke.jwgibbsbein" class="extiw" title="hdl:10079/fa/beinecke.jwgibbsbein">Josiah Willard Gibbs Papers</a>. General Collection, Beinecke Rare Book and Manuscript Library, Yale University.</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output 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href="/wiki/Template:Copley_Medallists_1901%E2%80%931950" title="Template:Copley Medallists 1901–1950"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Copley_Medallists_1901%E2%80%931950" title="Template talk:Copley Medallists 1901–1950"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Copley_Medallists_1901%E2%80%931950" title="Special:EditPage/Template:Copley Medallists 1901–1950"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Copley_Medallists_(1901–1950)" style="font-size:114%;margin:0 4em"><a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medallists</a> (1901–1950)</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Josiah Willard Gibbs</a> (1901)</li> <li><a href="/wiki/Joseph_Lister" title="Joseph Lister">Joseph Lister</a> (1902)</li> <li><a href="/wiki/Eduard_Suess" title="Eduard Suess">Eduard Suess</a> (1903)</li> <li><a href="/wiki/William_Crookes" title="William Crookes">William Crookes</a> (1904)</li> <li><a href="/wiki/Dmitri_Mendeleev" title="Dmitri Mendeleev">Dmitri Mendeleev</a> (1905)</li> <li><a href="/wiki/%C3%89lie_Metchnikoff" title="Élie Metchnikoff">Élie Metchnikoff</a> (1906)</li> <li><a href="/wiki/Albert_A._Michelson" title="Albert A. Michelson">Albert A. Michelson</a> (1907)</li> <li><a href="/wiki/Alfred_Russel_Wallace" title="Alfred Russel Wallace">Alfred Russel Wallace</a> (1908)</li> <li><a href="/wiki/George_William_Hill" title="George William Hill">George William Hill</a> (1909)</li> <li><a href="/wiki/Francis_Galton" title="Francis Galton">Francis Galton</a> (1910)</li> <li><a href="/wiki/George_Darwin" title="George Darwin">George Darwin</a> (1911)</li> <li><a href="/wiki/Felix_Klein" title="Felix Klein">Felix Klein</a> (1912)</li> <li><a href="/wiki/Ray_Lankester" title="Ray Lankester">Ray Lankester</a> (1913)</li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">J. J. Thomson</a> (1914)</li> <li><a href="/wiki/Ivan_Pavlov" title="Ivan Pavlov">Ivan Pavlov</a> (1915)</li> <li><a href="/wiki/James_Dewar" title="James Dewar">James Dewar</a> (1916)</li> <li><a href="/wiki/Pierre_Paul_%C3%89mile_Roux" class="mw-redirect" title="Pierre Paul Émile Roux">Pierre Paul Émile Roux</a> (1917)</li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Hendrik Lorentz</a> (1918)</li> <li><a href="/wiki/William_Bayliss" title="William Bayliss">William Bayliss</a> (1919)</li> <li><a href="/wiki/Horace_Tabberer_Brown" title="Horace Tabberer Brown">Horace Tabberer Brown</a> (1920)</li> <li><a href="/wiki/Joseph_Larmor" title="Joseph Larmor">Joseph Larmor</a> (1921)</li> <li><a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Ernest Rutherford</a> (1922)</li> <li><a href="/wiki/Horace_Lamb" title="Horace Lamb">Horace Lamb</a> (1923)</li> <li><a href="/wiki/Edward_Albert_Sharpey-Schafer" title="Edward Albert Sharpey-Schafer">Edward Albert Sharpey-Schafer</a> (1924)</li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> (1925)</li> <li><a href="/wiki/Frederick_Gowland_Hopkins" title="Frederick Gowland Hopkins">Frederick Gowland Hopkins</a> (1926)</li> <li><a href="/wiki/Charles_Scott_Sherrington" title="Charles Scott Sherrington">Charles Scott Sherrington</a> (1927)</li> <li><a href="/wiki/Charles_Algernon_Parsons" title="Charles Algernon Parsons">Charles Algernon Parsons</a> (1928)</li> <li><a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a> (1929)</li> <li><a href="/wiki/William_Henry_Bragg" title="William Henry Bragg">William Henry Bragg</a> (1930)</li> <li><a href="/wiki/Arthur_Schuster" title="Arthur Schuster">Arthur Schuster</a> (1931)</li> <li><a href="/wiki/George_Ellery_Hale" title="George Ellery Hale">George Ellery Hale</a> (1932)</li> <li><a href="/wiki/Theobald_Smith" title="Theobald Smith">Theobald Smith</a> (1933)</li> <li><a href="/wiki/John_Scott_Haldane" title="John Scott Haldane">John Scott Haldane</a> (1934)</li> <li><a href="/wiki/Charles_Thomson_Rees_Wilson" title="Charles Thomson Rees Wilson">Charles Thomson Rees Wilson</a> (1935)</li> <li><a href="/wiki/Arthur_Evans" title="Arthur Evans">Arthur Evans</a> (1936)</li> <li><a href="/wiki/Henry_Hallett_Dale" title="Henry Hallett Dale">Henry Hallett Dale</a> (1937)</li> <li><a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a> (1938)</li> <li><a href="/wiki/Thomas_Hunt_Morgan" title="Thomas Hunt Morgan">Thomas Hunt Morgan</a> (1939)</li> <li><a href="/wiki/Paul_Langevin" title="Paul Langevin">Paul Langevin</a> (1940)</li> <li><a href="/wiki/Thomas_Lewis_(cardiologist)" title="Thomas Lewis (cardiologist)">Thomas Lewis</a> (1941)</li> <li><a href="/wiki/Robert_Robinson_(chemist)" title="Robert Robinson (chemist)">Robert Robinson</a> (1942)</li> <li><a href="/wiki/Joseph_Barcroft" title="Joseph Barcroft">Joseph Barcroft</a> (1943)</li> <li><a href="/wiki/G._I._Taylor" title="G. I. Taylor">Geoffrey Ingram Taylor</a> (1944)</li> <li><a href="/wiki/Oswald_Avery" title="Oswald Avery">Oswald Avery</a> (1945)</li> <li><a href="/wiki/Edgar_Adrian" title="Edgar Adrian">Edgar Douglas Adrian</a> (1946)</li> <li><a href="/wiki/G._H._Hardy" title="G. H. Hardy">G. H. Hardy</a> (1947)</li> <li><a href="/wiki/Archibald_Hill" title="Archibald Hill">Archibald Hill</a> (1948)</li> <li><a href="/wiki/George_de_Hevesy" title="George de Hevesy">George de Hevesy</a> (1949)</li> <li><a href="/wiki/James_Chadwick" title="James Chadwick">James Chadwick</a> (1950)</li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Hall_of_Fame_for_Great_Americans_inductees" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Hall_of_Fame_for_Great_Americans" title="Template:Hall of Fame for Great Americans"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Hall_of_Fame_for_Great_Americans" title="Template talk:Hall of Fame for Great Americans"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Hall_of_Fame_for_Great_Americans" title="Special:EditPage/Template:Hall of Fame for Great Americans"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Hall_of_Fame_for_Great_Americans_inductees" style="font-size:114%;margin:0 4em"><a href="/wiki/Hall_of_Fame_for_Great_Americans" title="Hall of Fame for Great Americans">Hall of Fame for Great Americans</a> inductees</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/John_Adams" title="John Adams">John Adams</a></li> <li><a href="/wiki/John_Quincy_Adams" title="John Quincy Adams">John Quincy Adams</a></li> <li><a href="/wiki/Jane_Addams" title="Jane Addams">Jane Addams</a></li> <li><a href="/wiki/Louis_Agassiz" title="Louis Agassiz">Louis Agassiz</a></li> <li><a href="/wiki/Susan_B._Anthony" title="Susan B. Anthony">Susan B. Anthony</a></li> <li><a href="/wiki/John_James_Audubon" title="John James Audubon">John James Audubon</a></li> <li><a href="/wiki/George_Bancroft" title="George Bancroft">George Bancroft</a></li> <li><a href="/wiki/Clara_Barton" title="Clara Barton">Clara Barton</a></li> <li><a href="/wiki/Henry_Ward_Beecher" title="Henry Ward Beecher">Henry Ward Beecher</a></li> <li><a href="/wiki/Alexander_Graham_Bell" title="Alexander Graham Bell">Alexander Graham Bell</a></li> <li><a href="/wiki/Daniel_Boone" title="Daniel Boone">Daniel Boone</a></li> <li><a href="/wiki/Edwin_Booth" title="Edwin Booth">Edwin Booth</a></li> <li><a href="/wiki/Louis_Brandeis" title="Louis Brandeis">Louis Brandeis</a></li> <li><a href="/wiki/Phillips_Brooks" title="Phillips Brooks">Phillips Brooks</a></li> <li><a href="/wiki/William_Cullen_Bryant" title="William Cullen Bryant">William Cullen Bryant</a></li> <li><a href="/wiki/Luther_Burbank" title="Luther Burbank">Luther Burbank</a></li> <li><a href="/wiki/Andrew_Carnegie" title="Andrew Carnegie">Andrew Carnegie</a></li> <li><a href="/wiki/George_Washington_Carver" title="George Washington Carver">George Washington Carver</a></li> <li><a href="/wiki/William_Ellery_Channing" title="William Ellery Channing">William Ellery Channing</a></li> <li><a href="/wiki/Rufus_Choate" title="Rufus Choate">Rufus Choate</a></li> <li><a href="/wiki/Henry_Clay" title="Henry Clay">Henry Clay</a></li> <li><a href="/wiki/Grover_Cleveland" title="Grover Cleveland">Grover Cleveland</a></li> <li><a href="/wiki/James_Fenimore_Cooper" title="James Fenimore Cooper">James Fenimore Cooper</a></li> <li><a href="/wiki/Peter_Cooper" title="Peter Cooper">Peter Cooper</a></li> <li><a href="/wiki/Charlotte_Cushman" title="Charlotte Cushman">Charlotte Cushman</a></li> <li><a href="/wiki/James_Buchanan_Eads" title="James Buchanan Eads">James Buchanan Eads</a></li> <li><a href="/wiki/Thomas_Edison" title="Thomas Edison">Thomas Alva Edison</a></li> <li><a href="/wiki/Jonathan_Edwards_(theologian)" title="Jonathan Edwards (theologian)">Jonathan Edwards</a></li> <li><a href="/wiki/Ralph_Waldo_Emerson" title="Ralph Waldo Emerson">Ralph Waldo Emerson</a></li> <li><a href="/wiki/David_Farragut" title="David Farragut">David Farragut</a></li> <li><a href="/wiki/Stephen_Foster" title="Stephen Foster">Stephen Foster</a></li> <li><a href="/wiki/Benjamin_Franklin" title="Benjamin Franklin">Benjamin Franklin</a></li> <li><a href="/wiki/Robert_Fulton" title="Robert Fulton">Robert Fulton</a></li> <li><a class="mw-selflink selflink">Josiah W. Gibbs</a></li> <li><a href="/wiki/William_C._Gorgas" title="William C. Gorgas">William C. Gorgas</a></li> <li><a href="/wiki/Ulysses_S._Grant" title="Ulysses S. Grant">Ulysses S. Grant</a></li> <li><a href="/wiki/Asa_Gray" title="Asa Gray">Asa Gray</a></li> <li><a href="/wiki/Alexander_Hamilton" title="Alexander Hamilton">Alexander Hamilton</a></li> <li><a href="/wiki/Nathaniel_Hawthorne" title="Nathaniel Hawthorne">Nathaniel Hawthorne</a></li> <li><a href="/wiki/Joseph_Henry" title="Joseph Henry">Joseph Henry</a></li> <li><a href="/wiki/Patrick_Henry" title="Patrick Henry">Patrick Henry</a></li> <li><a href="/wiki/Oliver_Wendell_Holmes_Sr." title="Oliver Wendell Holmes Sr.">Oliver Wendell Holmes Sr.</a></li> <li><a href="/wiki/Oliver_Wendell_Holmes_Jr." title="Oliver Wendell Holmes Jr.">Oliver Wendell Holmes Jr.</a></li> <li><a href="/wiki/Mark_Hopkins_(educator)" title="Mark Hopkins (educator)">Mark Hopkins</a></li> <li><a href="/wiki/Elias_Howe" title="Elias Howe">Elias Howe</a></li> <li><a href="/wiki/Washington_Irving" title="Washington Irving">Washington Irving</a></li> <li><a href="/wiki/Andrew_Jackson" title="Andrew Jackson">Andrew Jackson</a></li> <li><a href="/wiki/Stonewall_Jackson" title="Stonewall Jackson">Thomas J. 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