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<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"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-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" title="Table of Contents" > <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" 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Available in 35 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-35" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">35 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%A7%D9%85_%D9%85%D8%BA%D9%84%D9%82" title="نظام مغلق – Arabic" lang="ar" hreflang="ar" data-title="نظام مغلق" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%97%D0%B0%D1%82%D0%B2%D0%BE%D1%80%D0%B5%D0%BD%D0%B0_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0" title="Затворена система – Bulgarian" lang="bg" hreflang="bg" data-title="Затворена система" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Sistema_tancat" title="Sistema tancat – Catalan" lang="ca" hreflang="ca" data-title="Sistema tancat" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Uzav%C5%99en%C3%A1_soustava" title="Uzavřená soustava – Czech" lang="cs" hreflang="cs" data-title="Uzavřená soustava" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Geschlossenes_System" title="Geschlossenes System – German" lang="de" hreflang="de" data-title="Geschlossenes System" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Suletud_s%C3%BCsteem_(f%C3%BC%C3%BCsika)" title="Suletud süsteem (füüsika) – Estonian" lang="et" hreflang="et" data-title="Suletud süsteem (füüsika)" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%BB%CE%B5%CE%B9%CF%83%CF%84%CF%8C_%CF%83%CF%8D%CF%83%CF%84%CE%B7%CE%BC%CE%B1" title="Κλειστό σύστημα – Greek" lang="el" hreflang="el" data-title="Κλειστό σύστημα" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Sistema_cerrado" title="Sistema cerrado – Spanish" lang="es" hreflang="es" data-title="Sistema cerrado" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Sistema_itxi" title="Sistema itxi – Basque" lang="eu" hreflang="eu" data-title="Sistema itxi" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B3%D8%A7%D9%85%D8%A7%D9%86%D9%87_%D8%A8%D8%B3%D8%AA%D9%87" title="سامانه بسته – Persian" lang="fa" hreflang="fa" data-title="سامانه بسته" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Syst%C3%A8me_ferm%C3%A9" title="Système fermé – French" lang="fr" hreflang="fr" data-title="Système fermé" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8B%AB%ED%9E%8C%EA%B3%84" title="닫힌계 – Korean" lang="ko" hreflang="ko" data-title="닫힌계" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%B5%E0%A5%83%E0%A4%A4_%E0%A4%A4%E0%A4%82%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="संवृत तंत्र – Hindi" lang="hi" hreflang="hi" data-title="संवृत तंत्र" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Termi%C4%8Dki_zatvoreni_sustav" title="Termički zatvoreni sustav – Croatian" lang="hr" hreflang="hr" data-title="Termički zatvoreni sustav" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sistem_tertutup" title="Sistem tertutup – Indonesian" lang="id" hreflang="id" data-title="Sistem tertutup" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Sistema_chiuso" title="Sistema chiuso – Italian" lang="it" hreflang="it" data-title="Sistema chiuso" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A9%E1%83%90%E1%83%99%E1%83%94%E1%83%A2%E1%83%98%E1%83%9A%E1%83%98_%E1%83%A1%E1%83%98%E1%83%A1%E1%83%A2%E1%83%94%E1%83%9B%E1%83%90" title="ჩაკეტილი სისტემა – Georgian" lang="ka" hreflang="ka" data-title="ჩაკეტილი სისტემა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Nosl%C4%93gta_sist%C4%93ma" title="Noslēgta sistēma – Latvian" lang="lv" hreflang="lv" data-title="Noslēgta sistēma" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Z%C3%A1rt_rendszer_(fizika)" title="Zárt rendszer (fizika) – Hungarian" lang="hu" hreflang="hu" data-title="Zárt rendszer (fizika)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B4%82%E0%B4%B5%E0%B5%83%E0%B4%A4%E0%B4%B5%E0%B5%8D%E0%B4%AF%E0%B5%82%E0%B4%B9%E0%B4%82" title="സംവൃതവ്യൂഹം – Malayalam" lang="ml" hreflang="ml" data-title="സംവൃതവ്യൂഹം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Gesloten_systeem" title="Gesloten systeem – Dutch" lang="nl" hreflang="nl" data-title="Gesloten systeem" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Lukket_system" title="Lukket system – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Lukket system" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Uk%C5%82ad_termodynamicznie_zamkni%C4%99ty" title="Układ termodynamicznie zamknięty – Polish" lang="pl" hreflang="pl" data-title="Układ termodynamicznie zamknięty" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Sistema_fechado" title="Sistema fechado – Portuguese" lang="pt" hreflang="pt" data-title="Sistema fechado" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Sistem_%C3%AEnchis" title="Sistem închis – Romanian" lang="ro" hreflang="ro" data-title="Sistem închis" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D1%80%D1%8B%D1%82%D0%B0%D1%8F_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Закрытая система (физика) – Russian" lang="ru" hreflang="ru" data-title="Закрытая система (физика)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Closed_system" title="Closed system – Simple English" lang="en-simple" hreflang="en-simple" data-title="Closed system" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Uzavret%C3%A1_s%C3%BAstava_(v%C3%BDmena_energie)" title="Uzavretá sústava (výmena energie) – Slovak" lang="sk" hreflang="sk" data-title="Uzavretá sústava (výmena energie)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Zaprti_sistem" title="Zaprti sistem – Slovenian" lang="sl" hreflang="sl" data-title="Zaprti sistem" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Zatvoreni_sistem" title="Zatvoreni sistem – Serbian" lang="sr" hreflang="sr" data-title="Zatvoreni sistem" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Slutet_system" title="Slutet system – Swedish" lang="sv" hreflang="sv" data-title="Slutet system" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kapal%C4%B1_sistem" title="Kapalı sistem – Turkish" lang="tr" hreflang="tr" data-title="Kapalı sistem" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D1%80%D0%B8%D1%82%D0%B0_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D1%96%D1%87%D0%BD%D0%B0_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0" title="Закрита термодинамічна система – Ukrainian" lang="uk" hreflang="uk" data-title="Закрита термодинамічна система" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%B0%81%E9%96%89%E7%B3%BB%E7%B5%B1" title="封閉系統 – Cantonese" lang="yue" hreflang="yue" data-title="封閉系統" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%B0%81%E9%96%89%E7%B3%BB%E7%B5%B1" title="封閉系統 – Chinese" lang="zh" hreflang="zh" data-title="封閉系統" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1468684#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> 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<div class="vector-body-before-content"> <div class="mw-indicators"> </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">Type of system</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">This article is about the physical sciences concept. For the computing concept, see <a href="/wiki/Closed_source_software" class="mw-redirect" title="Closed source software">Closed source software</a>.</div> <p>A <b>closed system</b> is a natural <a href="/wiki/Physical_system" title="Physical system">physical system</a> that does not allow transfer of <a href="/wiki/Matter" title="Matter">matter</a> in or out of the system, although – in the contexts of <a href="/wiki/Physics" title="Physics">physics</a>, <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, <a href="/wiki/Engineering" title="Engineering">engineering</a>, etc. – the transfer of energy (e.g. as work or heat) is allowed. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Physics">Physics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Closed_system&action=edit&section=1" title="Edit section: Physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="In_classical_mechanics">In classical mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Closed_system&action=edit&section=2" title="Edit section: In classical mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Theory_of_relativity" title="Theory of relativity">nonrelativistic</a> <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a>, a closed system is a <a href="/wiki/Physical_system" title="Physical system">physical system</a> that does not exchange any matter with its surroundings, and is not subject to any net <a href="/wiki/Force" title="Force">force</a> whose source is external to the system.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> A closed system in classical mechanics would be equivalent to an <a href="/wiki/Isolated_system" title="Isolated system">isolated system</a> in <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>. Closed systems are often used to limit the factors that can affect the results of a specific problem or experiment. </p> <div class="mw-heading mw-heading3"><h3 id="In_thermodynamics">In thermodynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Closed_system&action=edit&section=3" title="Edit section: In thermodynamics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Thermodynamic_system" title="Thermodynamic system">Thermodynamic system</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Diagram_Systems.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Diagram_Systems.svg/220px-Diagram_Systems.svg.png" decoding="async" width="220" height="122" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Diagram_Systems.svg/330px-Diagram_Systems.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Diagram_Systems.svg/440px-Diagram_Systems.svg.png 2x" data-file-width="300" data-file-height="167" /></a><figcaption>Properties of isolated, closed, and open systems in exchanging energy and matter</figcaption></figure> <p>In <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>, a closed system can exchange energy (as <a href="/wiki/Heat" title="Heat">heat</a> or <a href="/wiki/Mechanical_work" class="mw-redirect" title="Mechanical work">work</a>) but not <a href="/wiki/Matter" title="Matter">matter</a>, with its surroundings. An <a href="/wiki/Isolated_system" title="Isolated system">isolated system</a> cannot exchange any heat, work, or matter with the surroundings, while an <a href="/wiki/Thermodynamic_system#Open_system" title="Thermodynamic system">open system</a> can exchange energy and matter.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> (This scheme of definition of terms is not uniformly used, though it is convenient for some purposes. In particular, some writers use 'closed system' where 'isolated system' is used here.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>) </p><p>For a simple system, with only one type of particle (atom or molecule), a closed system amounts to a constant number of particles. However, for systems which are undergoing a <a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">chemical reaction</a>, there may be all sorts of molecules being generated and destroyed by the reaction process. In this case, the fact that the system is closed is expressed by stating that the total number of each elemental atom is conserved, no matter what kind of molecule it may be a part of. Mathematically: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{j=1}^{m}a_{ij}N_{j}=b_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </munderover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{j=1}^{m}a_{ij}N_{j}=b_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d660c86680283978f3fe212361ecf093cd337c8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:14.121ex; height:7.176ex;" alt="{\displaystyle \sum _{j=1}^{m}a_{ij}N_{j}=b_{i}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e42efe207e17a74b4c17b1aa0cced7a84501bec9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.776ex; height:2.843ex;" alt="{\displaystyle N_{j}}"></span> is the number of j-type molecules, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebea6cd2813c330c798921a2894b358f7b643917" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.707ex; height:2.343ex;" alt="{\displaystyle a_{ij}}"></span> is the number of atoms of element <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><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></span><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}"></span> in molecule <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40a8c2db2990a53c683e75961826167c5adac7c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.797ex; height:2.509ex;" alt="{\displaystyle b_{i}}"></span> is the total number of atoms of element <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><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></span><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}"></span> in the system, which remains constant, since the system is closed. There will be one such equation for each different element in the system. </p><p>In thermodynamics, a closed system is important for solving complicated thermodynamic problems. It allows the elimination of some external factors that could alter the results of the experiment or problem thus simplifying it. A closed system can also be used in situations where <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a> is required to simplify the situation. </p> <div class="mw-heading mw-heading3"><h3 id="In_quantum_physics">In quantum physics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Closed_system&action=edit&section=4" title="Edit section: In quantum physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a></div><p>This equation, called <a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger's equation</a>, describes the behavior of an isolated or closed quantum system, that is, by definition, a system which does not interchange information (i.e. energy and/or matter) with another system. So if an isolated system is in some pure state |ψ(t) ∈ H at time t, where H denotes the Hilbert space of the system, the time evolution of this state (between two consecutive measurements).<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\hbar {\frac {\partial }{\partial t}}\Psi (\mathbf {r} ,t)={\hat {H}}\Psi (\mathbf {r} ,t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {\partial }{\partial t}}\Psi (\mathbf {r} ,t)={\hat {H}}\Psi (\mathbf {r} ,t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/327546c3f8bd78d7d533c5c04f7602086862dfd4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:23.451ex; height:5.509ex;" alt="{\displaystyle i\hbar {\frac {\partial }{\partial t}}\Psi (\mathbf {r} ,t)={\hat {H}}\Psi (\mathbf {r} ,t)}"></span> </p><p>where <span class="texhtml"><i>i</i></span> is the <a href="/wiki/Imaginary_unit" title="Imaginary unit">imaginary unit</a>, <span class="texhtml"><i>ħ</i></span> is the <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a> divided by <span class="texhtml">2π</span>, the symbol <span class="texhtml"><style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">∂</span><span class="sr-only">/</span><span class="den">∂<i>t</i></span></span>⁠</span></span> indicates a <a href="/wiki/Partial_derivative" title="Partial derivative">partial derivative</a> with respect to <a href="/wiki/Time" title="Time">time</a> <span class="texhtml"><i>t</i></span>, <span class="texhtml">Ψ</span> (the Greek letter <a href="/wiki/Psi_(letter)" class="mw-redirect" title="Psi (letter)">psi</a>) is the <a href="/wiki/Wave_function" title="Wave function">wave function</a> of the quantum system, and <span class="texhtml"><i>Ĥ</i></span> is the <a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonian</a> <a href="/wiki/Operator_(physics)" title="Operator (physics)">operator</a> (which characterizes the total energy of any given wave function and takes different forms depending on the situation). </p> <div class="mw-heading mw-heading2"><h2 id="In_chemistry">In chemistry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Closed_system&action=edit&section=5" title="Edit section: In chemistry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In chemistry, a closed system is where no reactants or products can escape, only heat can be exchanged freely (e.g. an ice cooler). A closed system can be used when conducting chemical experiments where temperature is not a factor (i.e. reaching <a href="/wiki/Thermal_equilibrium" title="Thermal equilibrium">thermal equilibrium</a>). </p> <div class="mw-heading mw-heading2"><h2 id="In_engineering">In engineering</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Closed_system&action=edit&section=6" title="Edit section: In engineering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In an <a href="/wiki/Engineering" title="Engineering">engineering</a> context, a closed system is a bound system, i.e. defined, in which every input is known and every resultant is known (or can be known) within a specific time. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Closed_system&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Glossary_of_systems_theory" title="Glossary of systems theory">Glossary of systems theory</a></li> <li><a href="/wiki/Dynamical_system" title="Dynamical system">Dynamical system</a></li> <li><a href="/wiki/Isolated_system" title="Isolated system">Isolated system</a></li> <li><a href="/wiki/Open_system_(systems_theory)" title="Open system (systems theory)">Open system (systems theory)</a></li> <li><a href="/wiki/Sense_and_Respond" class="mw-redirect" title="Sense and Respond">Sense and Respond</a></li> <li><a href="/wiki/Thermodynamic_system" title="Thermodynamic system">Thermodynamic system</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Closed_system&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFRanaP.S._Joag1991" class="citation book cs1">Rana, N.C.; P.S. Joag (1991). <i>Classical Mechanics</i>. p. 78. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-460315-4" title="Special:BookSources/978-0-07-460315-4"><bdi>978-0-07-460315-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Classical+Mechanics&rft.pages=78&rft.date=1991&rft.isbn=978-0-07-460315-4&rft.aulast=Rana&rft.aufirst=N.C.&rft.au=P.S.+Joag&rfr_id=info%3Asid%2Fen.wikipedia.org%3AClosed+system" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLandauE.M._Lifshitz1976" class="citation book cs1"><a href="/wiki/Lev_Landau" title="Lev Landau">Landau, L.D.</a>; E.M. Lifshitz (1976). <i>Mechanics</i> (third ed.). Butterworth-Heinemann. p. 8. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7506-2896-9" title="Special:BookSources/978-0-7506-2896-9"><bdi>978-0-7506-2896-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mechanics&rft.pages=8&rft.edition=third&rft.pub=Butterworth-Heinemann&rft.date=1976&rft.isbn=978-0-7506-2896-9&rft.aulast=Landau&rft.aufirst=L.D.&rft.au=E.M.+Lifshitz&rfr_id=info%3Asid%2Fen.wikipedia.org%3AClosed+system" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a href="/wiki/Ilya_Prigogine" title="Ilya Prigogine">Prigogine, I.</a>, Defay, R. (1950/1954). <i>Chemical Thermodynamics</i>, Longmans, Green & Co, London, p. 66.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a href="/wiki/L%C3%A1szl%C3%B3_Tisza" title="László Tisza">Tisza, L.</a> (1966). <i>Generalized Thermodynamics</i>, M.I.T Press, Cambridge MA, pp. 112–113.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a href="/wiki/Edward_A._Guggenheim" title="Edward A. Guggenheim">Guggenheim, E.A.</a> (1949/1967). <i>Thermodynamics. An Advanced Treatment for Chemists and Physicists</i>, (1st edition 1949) 5th edition 1967, North-Holland, Amsterdam, p. 14.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Münster, A. (1970). <i>Classical Thermodynamics</i>, translated by E.S. Halberstadt, Wiley–Interscience, London, pp. 6–7.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of <i>Thermodynamics</i>, pages 1–97 of volume 1, ed. W. Jost, of <i>Physical Chemistry. An Advanced Treatise</i>, ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081, p. 3.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Tschoegl, N.W. (2000). <i>Fundamentals of Equilibrium and Steady-State Thermodynamics</i>, Elsevier, Amsterdam, <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/0-444-50426-5" title="Special:BookSources/0-444-50426-5">0-444-50426-5</a>, p. 5.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Silbey, R.J., <a href="/wiki/Robert_A._Alberty" title="Robert A. Alberty">Alberty, R.A.</a>, Bawendi, M.G. (1955/2005). <i>Physical Chemistry</i>, fourth edition, Wiley, Hoboken NJ, p. 4.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><a href="/wiki/Herbert_Callen" title="Herbert Callen">Callen, H.B.</a> (1960/1985). <i>Thermodynamics and an Introduction to Thermostatistics</i>, (1st edition 1960) 2nd edition 1985, Wiley, New York, <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/0-471-86256-8" title="Special:BookSources/0-471-86256-8">0-471-86256-8</a>, p. 17.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><a href="/wiki/Dirk_ter_Haar" title="Dirk ter Haar">ter Haar, D.</a>, <a href="/wiki/Harald_Wergeland" title="Harald Wergeland">Wergeland, H.</a> (1966). <i>Elements of Thermodynamics</i>, Addison-Wesley Publishing, Reading MA, p. 43.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRivasHuelga2011" class="citation book cs1">Rivas, Ángel; <a href="/wiki/Susana_F._Huelga" title="Susana F. Huelga">Huelga, Susana F.</a> (October 2011). <i>Open Quantum Systems</i>. Berlin Heidelberg: Springer-Verlag. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-23354-8" title="Special:BookSources/978-3-642-23354-8"><bdi>978-3-642-23354-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Open+Quantum+Systems&rft.place=Berlin+Heidelberg&rft.pub=Springer-Verlag&rft.date=2011-10&rft.isbn=978-3-642-23354-8&rft.aulast=Rivas&rft.aufirst=%C3%81ngel&rft.au=Huelga%2C+Susana+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AClosed+system" class="Z3988"></span></span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Closed_system&oldid=1258616864">https://en.wikipedia.org/w/index.php?title=Closed_system&oldid=1258616864</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Cybernetics" title="Category:Cybernetics">Cybernetics</a></li><li><a href="/wiki/Category:Systems_theory" title="Category:Systems theory">Systems theory</a></li><li><a href="/wiki/Category:Thermodynamic_systems" title="Category:Thermodynamic systems">Thermodynamic systems</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 20 November 2024, at 18:10<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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