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id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">보이기</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ko.wikipedia.org&uselang=ko" class=""><span>기부</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EA%B3%84%EC%A0%95%EB%A7%8C%EB%93%A4%EA%B8%B0&returnto=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC" title="계정을 만들고 로그인하는 것이 좋습니다. 하지만 필수는 아닙니다" class=""><span>계정 만들기</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EB%A1%9C%EA%B7%B8%EC%9D%B8&returnto=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC" title="위키백과에 로그인하면 여러가지 편리한 기능을 사용할 수 있습니다. [o]" accesskey="o" class=""><span>로그인</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="더 많은 옵션" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="개인 도구" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">개인 도구</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="사용자 메뉴" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ko.wikipedia.org&uselang=ko"><span>기부</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EA%B3%84%EC%A0%95%EB%A7%8C%EB%93%A4%EA%B8%B0&returnto=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC" title="계정을 만들고 로그인하는 것이 좋습니다. 하지만 필수는 아닙니다"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>계정 만들기</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EB%A1%9C%EA%B7%B8%EC%9D%B8&returnto=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC" title="위키백과에 로그인하면 여러가지 편리한 기능을 사용할 수 있습니다. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>로그인</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 로그아웃한 편집자를 위한 문서 <a href="/wiki/%EB%8F%84%EC%9B%80%EB%A7%90:%EC%86%8C%EA%B0%9C" aria-label="편집에 관해 더 알아보기"><span>더 알아보기</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%82%B4%EA%B8%B0%EC%97%AC" title="이 IP 주소의 편집 목록 [y]" accesskey="y"><span>기여</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%82%B4%EC%82%AC%EC%9A%A9%EC%9E%90%ED%86%A0%EB%A1%A0" title="현재 사용하는 IP 주소에 대한 토론 문서 [n]" accesskey="n"><span>토론</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="사이트"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="목차" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">목차</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">숨기기</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">처음 위치</div> </a> </li> <li id="toc-정의" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#정의"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>정의</span> </div> </a> <button aria-controls="toc-정의-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>정의 하위섹션 토글하기</span> </button> <ul id="toc-정의-sublist" class="vector-toc-list"> <li id="toc-열역학적_정의" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#열역학적_정의"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>열역학적 정의</span> </div> </a> <ul id="toc-열역학적_정의-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-통계역학적_정의" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#통계역학적_정의"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>통계역학적 정의</span> </div> </a> <ul id="toc-통계역학적_정의-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-양자역학적_정의" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#양자역학적_정의"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>양자역학적 정의</span> </div> </a> <ul id="toc-양자역학적_정의-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-블랙홀의_엔트로피" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#블랙홀의_엔트로피"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>블랙홀의 엔트로피</span> </div> </a> <ul id="toc-블랙홀의_엔트로피-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-성질" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#성질"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>성질</span> </div> </a> <ul id="toc-성질-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-열_엔트로피와_위치_엔트로피" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#열_엔트로피와_위치_엔트로피"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>열 엔트로피와 위치 엔트로피</span> </div> </a> <ul id="toc-열_엔트로피와_위치_엔트로피-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-엔트로피에_관한_작품" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#엔트로피에_관한_작품"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>엔트로피에 관한 작품</span> </div> </a> <ul id="toc-엔트로피에_관한_작품-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-같이_보기" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#같이_보기"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>같이 보기</span> </div> </a> <ul id="toc-같이_보기-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-주해" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#주해"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>주해</span> </div> </a> <ul id="toc-주해-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-각주" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#각주"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>각주</span> </div> </a> <ul id="toc-각주-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-외부_링크" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#외부_링크"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>외부 링크</span> </div> </a> <ul id="toc-외부_링크-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="목차" 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="목차 토글" > <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" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">목차 토글</span> </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"><span class="mw-page-title-main">엔트로피</span></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="다른 언어로 문서를 방문합니다. 90개 언어로 읽을 수 있습니다" > <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-90" 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">90개 언어</span> </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/Entropie" title="Entropie – 아프리칸스어" lang="af" hreflang="af" data-title="Entropie" data-language-autonym="Afrikaans" data-language-local-name="아프리칸스어" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%8A%95%E1%89%B5%E1%88%A8%E1%89%A2" title="አንትረቢ – 암하라어" lang="am" hreflang="am" data-title="አንትረቢ" data-language-autonym="አማርኛ" data-language-local-name="암하라어" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A5%D9%86%D8%AA%D8%B1%D9%88%D8%A8%D9%8A%D8%A7" title="إنتروبيا – 아랍어" lang="ar" hreflang="ar" data-title="إنتروبيا" data-language-autonym="العربية" data-language-local-name="아랍어" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%84%D9%88%D9%86%D8%B7%D8%B1%D9%88%D9%BE%D9%8A" title="لونطروپي – 모로코 아랍어" lang="ary" hreflang="ary" data-title="لونطروپي" data-language-autonym="الدارجة" data-language-local-name="모로코 아랍어" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Entrop%C3%ADa" title="Entropía – 아스투리아어" lang="ast" hreflang="ast" data-title="Entropía" data-language-autonym="Asturianu" data-language-local-name="아스투리아어" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Entropiya" title="Entropiya – 아제르바이잔어" lang="az" hreflang="az" data-title="Entropiya" data-language-autonym="Azərbaycanca" data-language-local-name="아제르바이잔어" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Entropie_(Thermodynamik)" title="Entropie (Thermodynamik) – Bavarian" lang="bar" hreflang="bar" data-title="Entropie (Thermodynamik)" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Entropiya" title="Entropiya – Central Bikol" lang="bcl" hreflang="bcl" data-title="Entropiya" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BD%D1%82%D1%80%D0%B0%D0%BF%D1%96%D1%8F" title="Энтрапія – 벨라루스어" lang="be" hreflang="be" data-title="Энтрапія" data-language-autonym="Беларуская" data-language-local-name="벨라루스어" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%AD%D0%BD%D1%82%D1%80%D0%B0%D0%BF%D1%96%D1%8F" title="Энтрапія – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Энтрапія" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D0%B8%D1%8F" title="Ентропия – 불가리아어" lang="bg" hreflang="bg" data-title="Ентропия" data-language-autonym="Български" data-language-local-name="불가리아어" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%B6%E0%A7%83%E0%A6%99%E0%A7%8D%E0%A6%96%E0%A6%B2%E0%A6%BE-%E0%A6%AE%E0%A6%BE%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%BE" title="বিশৃঙ্খলা-মাত্রা – 벵골어" lang="bn" hreflang="bn" data-title="বিশৃঙ্খলা-মাত্রা" data-language-autonym="বাংলা" data-language-local-name="벵골어" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Entropiezh" title="Entropiezh – 브르타뉴어" lang="br" hreflang="br" data-title="Entropiezh" data-language-autonym="Brezhoneg" data-language-local-name="브르타뉴어" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Entropija" title="Entropija – 보스니아어" lang="bs" hreflang="bs" data-title="Entropija" data-language-autonym="Bosanski" data-language-local-name="보스니아어" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Entropia" title="Entropia – 카탈로니아어" lang="ca" hreflang="ca" data-title="Entropia" data-language-autonym="Català" data-language-local-name="카탈로니아어" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%DB%8E%D9%86%D8%AA%D8%B1%DB%86%D9%BE%DB%8C" title="ئێنترۆپی – 소라니 쿠르드어" lang="ckb" hreflang="ckb" data-title="ئێنترۆپی" data-language-autonym="کوردی" data-language-local-name="소라니 쿠르드어" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Entropie" title="Entropie – 체코어" lang="cs" hreflang="cs" data-title="Entropie" data-language-autonym="Čeština" data-language-local-name="체코어" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%AD%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D0%B8" title="Энтропи – 추바시어" lang="cv" hreflang="cv" data-title="Энтропи" data-language-autonym="Чӑвашла" data-language-local-name="추바시어" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Entropi" title="Entropi – 덴마크어" lang="da" hreflang="da" data-title="Entropi" data-language-autonym="Dansk" data-language-local-name="덴마크어" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Entropie" title="Entropie – 독일어" lang="de" hreflang="de" data-title="Entropie" data-language-autonym="Deutsch" data-language-local-name="독일어" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BD%CF%84%CF%81%CE%BF%CF%80%CE%AF%CE%B1" title="Εντροπία – 그리스어" lang="el" hreflang="el" data-title="Εντροπία" data-language-autonym="Ελληνικά" data-language-local-name="그리스어" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Entropy" title="Entropy – 영어" lang="en" hreflang="en" data-title="Entropy" data-language-autonym="English" data-language-local-name="영어" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Entropio" title="Entropio – 에스페란토어" lang="eo" hreflang="eo" data-title="Entropio" data-language-autonym="Esperanto" data-language-local-name="에스페란토어" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Entrop%C3%ADa" title="Entropía – 스페인어" lang="es" hreflang="es" data-title="Entropía" data-language-autonym="Español" data-language-local-name="스페인어" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Entroopia" title="Entroopia – 에스토니아어" lang="et" hreflang="et" data-title="Entroopia" data-language-autonym="Eesti" data-language-local-name="에스토니아어" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Entropia" title="Entropia – 바스크어" lang="eu" hreflang="eu" data-title="Entropia" data-language-autonym="Euskara" data-language-local-name="바스크어" 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%A2%D9%86%D8%AA%D8%B1%D9%88%D9%BE%DB%8C" title="آنتروپی – 페르시아어" lang="fa" hreflang="fa" data-title="آنتروپی" data-language-autonym="فارسی" data-language-local-name="페르시아어" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Entropia" title="Entropia – 핀란드어" lang="fi" hreflang="fi" data-title="Entropia" data-language-autonym="Suomi" data-language-local-name="핀란드어" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Entropie_(thermodynamique)" title="Entropie (thermodynamique) – 프랑스어" lang="fr" hreflang="fr" data-title="Entropie (thermodynamique)" data-language-autonym="Français" data-language-local-name="프랑스어" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Eantr%C3%B3pacht" title="Eantrópacht – 아일랜드어" lang="ga" hreflang="ga" data-title="Eantrópacht" data-language-autonym="Gaeilge" data-language-local-name="아일랜드어" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Entrop%C3%ADa" title="Entropía – 갈리시아어" lang="gl" hreflang="gl" data-title="Entropía" data-language-autonym="Galego" data-language-local-name="갈리시아어" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gor mw-list-item"><a href="https://gor.wikipedia.org/wiki/Entropy" title="Entropy – 고론탈로어" lang="gor" hreflang="gor" data-title="Entropy" data-language-autonym="Bahasa Hulontalo" data-language-local-name="고론탈로어" class="interlanguage-link-target"><span>Bahasa Hulontalo</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Entroapaght" title="Entroapaght – 맹크스어" lang="gv" hreflang="gv" data-title="Entroapaght" data-language-autonym="Gaelg" data-language-local-name="맹크스어" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A0%D7%98%D7%A8%D7%95%D7%A4%D7%99%D7%94" title="אנטרופיה – 히브리어" lang="he" hreflang="he" data-title="אנטרופיה" data-language-autonym="עברית" data-language-local-name="히브리어" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%8F%E0%A4%A8%E0%A5%8D%E0%A4%9F%E0%A5%8D%E0%A4%B0%E0%A5%89%E0%A4%AA%E0%A5%80" title="एन्ट्रॉपी – 힌디어" lang="hi" hreflang="hi" data-title="एन्ट्रॉपी" data-language-autonym="हिन्दी" data-language-local-name="힌디어" 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/Entropija" title="Entropija – 크로아티아어" lang="hr" hreflang="hr" data-title="Entropija" data-language-autonym="Hrvatski" data-language-local-name="크로아티아어" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Antwopi" title="Antwopi – 아이티어" lang="ht" hreflang="ht" data-title="Antwopi" data-language-autonym="Kreyòl ayisyen" data-language-local-name="아이티어" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Entr%C3%B3pia" title="Entrópia – 헝가리어" lang="hu" hreflang="hu" data-title="Entrópia" data-language-autonym="Magyar" data-language-local-name="헝가리어" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B7%D5%B6%D5%BF%D6%80%D5%B8%D5%BA%D5%AB%D5%A1" title="Էնտրոպիա – 아르메니아어" lang="hy" hreflang="hy" data-title="Էնտրոպիա" data-language-autonym="Հայերեն" data-language-local-name="아르메니아어" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Entropia" title="Entropia – 인터링구아" lang="ia" hreflang="ia" data-title="Entropia" data-language-autonym="Interlingua" data-language-local-name="인터링구아" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Entropi" title="Entropi – 인도네시아어" lang="id" hreflang="id" data-title="Entropi" data-language-autonym="Bahasa Indonesia" data-language-local-name="인도네시아어" 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/Entropia" title="Entropia – 이탈리아어" lang="it" hreflang="it" data-title="Entropia" data-language-autonym="Italiano" data-language-local-name="이탈리아어" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A8%E3%83%B3%E3%83%88%E3%83%AD%E3%83%94%E3%83%BC" title="エントロピー – 일본어" lang="ja" hreflang="ja" data-title="エントロピー" data-language-autonym="日本語" data-language-local-name="일본어" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%97%E1%83%94%E1%83%A0%E1%83%9B%E1%83%9D%E1%83%93%E1%83%98%E1%83%9C%E1%83%90%E1%83%9B%E1%83%98%E1%83%99%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%94%E1%83%9C%E1%83%A2%E1%83%A0%E1%83%9D%E1%83%9E%E1%83%98%E1%83%90" title="თერმოდინამიკური ენტროპია – 조지아어" lang="ka" hreflang="ka" data-title="თერმოდინამიკური ენტროპია" data-language-autonym="ქართული" data-language-local-name="조지아어" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AD%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D0%B8%D1%8F" title="Энтропия – 카자흐어" lang="kk" hreflang="kk" data-title="Энтропия" data-language-autonym="Қазақша" data-language-local-name="카자흐어" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%8E%E0%B2%82%E0%B2%9F%E0%B3%8D%E0%B2%B0%E0%B3%8B%E0%B2%AA%E0%B2%BF" title="ಎಂಟ್ರೋಪಿ – 칸나다어" lang="kn" hreflang="kn" data-title="ಎಂಟ್ರೋಪಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="칸나다어" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Entrop%C3%AE" title="Entropî – 쿠르드어" lang="ku" hreflang="ku" data-title="Entropî" data-language-autonym="Kurdî" data-language-local-name="쿠르드어" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%AD%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D0%B8%D1%8F" title="Энтропия – 키르기스어" lang="ky" hreflang="ky" data-title="Энтропия" data-language-autonym="Кыргызча" data-language-local-name="키르기스어" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Entropia" title="Entropia – 라틴어" lang="la" hreflang="la" data-title="Entropia" data-language-autonym="Latina" data-language-local-name="라틴어" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Entrupia" title="Entrupia – Lombard" lang="lmo" hreflang="lmo" data-title="Entrupia" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Entropija" title="Entropija – 리투아니아어" lang="lt" hreflang="lt" data-title="Entropija" data-language-autonym="Lietuvių" data-language-local-name="리투아니아어" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Entropija" title="Entropija – 라트비아어" lang="lv" hreflang="lv" data-title="Entropija" data-language-autonym="Latviešu" data-language-local-name="라트비아어" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%95%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D0%B8%D1%98%D0%B0" title="Ентропија – 마케도니아어" lang="mk" hreflang="mk" data-title="Ентропија" data-language-autonym="Македонски" data-language-local-name="마케도니아어" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%89%E0%B4%A4%E0%B5%8D%E0%B4%95%E0%B5%8D%E0%B4%B0%E0%B4%AE%E0%B4%82" title="ഉത്ക്രമം – 말라얄람어" lang="ml" hreflang="ml" data-title="ഉത്ക്രമം" data-language-autonym="മലയാളം" data-language-local-name="말라얄람어" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%AD%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D0%B8" title="Энтропи – 몽골어" lang="mn" hreflang="mn" data-title="Энтропи" data-language-autonym="Монгол" data-language-local-name="몽골어" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%84%E1%80%BA%E1%80%91%E1%80%9B%E1%80%AD%E1%80%AF%E1%80%95%E1%80%AE" title="အင်ထရိုပီ – 버마어" lang="my" hreflang="my" data-title="အင်ထရိုပီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="버마어" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Entropie" title="Entropie – 네덜란드어" lang="nl" hreflang="nl" data-title="Entropie" data-language-autonym="Nederlands" data-language-local-name="네덜란드어" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Entropi" title="Entropi – 노르웨이어(니노르스크)" lang="nn" hreflang="nn" data-title="Entropi" data-language-autonym="Norsk nynorsk" data-language-local-name="노르웨이어(니노르스크)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Entropi" title="Entropi – 노르웨이어(보크말)" lang="nb" hreflang="nb" data-title="Entropi" data-language-autonym="Norsk bokmål" data-language-local-name="노르웨이어(보크말)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Entropia_(termodinamica)" title="Entropia (termodinamica) – 오크어" lang="oc" hreflang="oc" data-title="Entropia (termodinamica)" data-language-autonym="Occitan" data-language-local-name="오크어" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Intiroopii" title="Intiroopii – 오로모어" lang="om" hreflang="om" data-title="Intiroopii" data-language-autonym="Oromoo" data-language-local-name="오로모어" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%90%E0%A8%A8%E0%A8%9F%E0%A9%8D%E0%A8%B0%E0%A8%BE%E0%A8%AA%E0%A9%80" title="ਐਨਟ੍ਰਾਪੀ – 펀잡어" lang="pa" hreflang="pa" data-title="ਐਨਟ੍ਰਾਪੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="펀잡어" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Entropia" title="Entropia – 폴란드어" lang="pl" hreflang="pl" data-title="Entropia" data-language-autonym="Polski" data-language-local-name="폴란드어" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%A7%DB%90%D9%86%D9%BC%D8%B1%D9%88%D9%BE%D9%8A" title="اېنټروپي – 파슈토어" lang="ps" hreflang="ps" data-title="اېنټروپي" data-language-autonym="پښتو" data-language-local-name="파슈토어" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Entropia" title="Entropia – 포르투갈어" lang="pt" hreflang="pt" data-title="Entropia" data-language-autonym="Português" data-language-local-name="포르투갈어" 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/Entropie" title="Entropie – 루마니아어" lang="ro" hreflang="ro" data-title="Entropie" data-language-autonym="Română" data-language-local-name="루마니아어" 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%AD%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D0%B8%D1%8F" title="Энтропия – 러시아어" lang="ru" hreflang="ru" data-title="Энтропия" data-language-autonym="Русский" data-language-local-name="러시아어" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://sc.wikipedia.org/wiki/Entropia" title="Entropia – 사르디니아어" lang="sc" hreflang="sc" data-title="Entropia" data-language-autonym="Sardu" data-language-local-name="사르디니아어" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Intrup%C3%ACa" title="Intrupìa – 시칠리아어" lang="scn" hreflang="scn" data-title="Intrupìa" data-language-autonym="Sicilianu" data-language-local-name="시칠리아어" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Entropija" title="Entropija – 세르비아-크로아티아어" lang="sh" hreflang="sh" data-title="Entropija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="세르비아-크로아티아어" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Entropy" title="Entropy – Simple English" lang="en-simple" hreflang="en-simple" data-title="Entropy" 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/Entropia" title="Entropia – 슬로바키아어" lang="sk" hreflang="sk" data-title="Entropia" data-language-autonym="Slovenčina" data-language-local-name="슬로바키아어" 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/Entropija_(klasi%C4%8Dna_termodinamika)" title="Entropija (klasična termodinamika) – 슬로베니아어" lang="sl" hreflang="sl" data-title="Entropija (klasična termodinamika)" data-language-autonym="Slovenščina" data-language-local-name="슬로베니아어" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Entropia" title="Entropia – 알바니아어" lang="sq" hreflang="sq" data-title="Entropia" data-language-autonym="Shqip" data-language-local-name="알바니아어" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%95%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D0%B8%D1%98%D0%B0" title="Ентропија – 세르비아어" lang="sr" hreflang="sr" data-title="Ентропија" data-language-autonym="Српски / srpski" data-language-local-name="세르비아어" 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/Entropi" title="Entropi – 스웨덴어" lang="sv" hreflang="sv" data-title="Entropi" data-language-autonym="Svenska" data-language-local-name="스웨덴어" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AE%BF%E0%AE%A4%E0%AE%B1%E0%AE%AE%E0%AF%8D" title="சிதறம் – 타밀어" lang="ta" hreflang="ta" data-title="சிதறம்" data-language-autonym="தமிழ்" data-language-local-name="타밀어" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%8E%E0%B0%82%E0%B0%9F%E0%B1%8D%E0%B0%B0%E0%B1%8B%E0%B0%AA%E0%B0%BF" title="ఎంట్రోపి – 텔루구어" lang="te" hreflang="te" data-title="ఎంట్రోపి" data-language-autonym="తెలుగు" data-language-local-name="텔루구어" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%AD%E0%B8%99%E0%B9%82%E0%B8%97%E0%B8%A3%E0%B8%9B%E0%B8%B5" title="เอนโทรปี – 태국어" lang="th" hreflang="th" data-title="เอนโทรปี" data-language-autonym="ไทย" data-language-local-name="태국어" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Entropi" title="Entropi – 터키어" lang="tr" hreflang="tr" data-title="Entropi" data-language-autonym="Türkçe" data-language-local-name="터키어" 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%95%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D1%96%D1%8F" title="Ентропія – 우크라이나어" lang="uk" hreflang="uk" data-title="Ентропія" data-language-autonym="Українська" data-language-local-name="우크라이나어" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D9%86%D9%B9%D8%B1%D9%88%D9%BE%DB%8C" title="انٹروپی – 우르두어" lang="ur" hreflang="ur" data-title="انٹروپی" data-language-autonym="اردو" data-language-local-name="우르두어" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Entropiya" title="Entropiya – 우즈베크어" lang="uz" hreflang="uz" data-title="Entropiya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="우즈베크어" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Entropy" title="Entropy – 베트남어" lang="vi" hreflang="vi" data-title="Entropy" data-language-autonym="Tiếng Việt" data-language-local-name="베트남어" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%86%B5" title="熵 – 우어" lang="wuu" hreflang="wuu" data-title="熵" data-language-autonym="吴语" data-language-local-name="우어" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A2%D7%A0%D7%98%D7%A8%D7%90%D7%A4%D7%99%D7%A2" title="ענטראפיע – 이디시어" lang="yi" hreflang="yi" data-title="ענטראפיע" data-language-autonym="ייִדיש" data-language-local-name="이디시어" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%86%B5" title="熵 – 중국어" lang="zh" hreflang="zh" data-title="熵" data-language-autonym="中文" data-language-local-name="중국어" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%86%B5" title="熵 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="熵" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Entropy" title="Entropy – 민난어" lang="nan" hreflang="nan" data-title="Entropy" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="민난어" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%86%B5" title="熵 – 광둥어" lang="yue" hreflang="yue" data-title="熵" data-language-autonym="粵語" data-language-local-name="광둥어" class="interlanguage-link-target"><span>粵語</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/Q45003#sitelinks-wikipedia" title="언어 간 링크 편집" class="wbc-editpage">링크 편집</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> 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</p> <div class="dablink hatnote"><span typeof="mw:File"><a href="/wiki/%EC%9C%84%ED%82%A4%EB%B0%B1%EA%B3%BC:%EB%8F%99%EC%9D%8C%EC%9D%B4%EC%9D%98%EC%96%B4_%EB%AC%B8%EC%84%9C" title="위키백과:동음이의어 문서"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/23px-Disambig_grey.svg.png" decoding="async" width="23" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/35px-Disambig_grey.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/46px-Disambig_grey.svg.png 2x" data-file-width="260" data-file-height="200" /></a></span> 다른 뜻에 대해서는 <a href="/wiki/%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC_(%EB%8F%99%EC%9D%8C%EC%9D%B4%EC%9D%98)" class="mw-disambig" title="엔트로피 (동음이의)">엔트로피 (동음이의)</a> 문서를 참고하십시오.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Ice_water.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Ice_water.jpg/220px-Ice_water.jpg" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Ice_water.jpg/330px-Ice_water.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Ice_water.jpg/440px-Ice_water.jpg 2x" data-file-width="768" data-file-height="1024" /></a><figcaption>얼음이 녹으면 엔트로피가 증가한다.</figcaption></figure> <p><b>엔트로피</b>(<span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">entropy</span>, <span style="font-size: smaller;"><a href="/wiki/%EB%8F%85%EC%9D%BC%EC%96%B4" title="독일어">독일어</a>: </span><span lang="de">entropie</span>)는 <a href="/wiki/%EA%B3%84_(%EB%AC%BC%EB%A6%AC%ED%95%99)#열역학의_계" class="mw-redirect" title="계 (물리학)">열역학적 계</a>의 유용하지 않은 (<a href="/wiki/%EC%9D%BC_(%EB%AC%BC%EB%A6%AC)" class="mw-redirect" title="일 (물리)">일</a>로 변환할 수 없는) <a href="/wiki/%EC%97%90%EB%84%88%EC%A7%80" title="에너지">에너지</a>의 흐름을 설명할 때 이용되는 <a href="/wiki/%EC%83%81%ED%83%9C_%ED%95%A8%EC%88%98" title="상태 함수">상태 함수</a>다. <a href="/wiki/%ED%86%B5%EA%B3%84%EC%97%AD%ED%95%99" title="통계역학">통계역학</a>적으로, 주어진 거시적 상태에 대응하는 미시적 상태의 수의 <a href="/wiki/%EB%A1%9C%EA%B7%B8" class="mw-disambig" title="로그">로그</a>로 생각할 수 있다. 엔트로피는 일반적으로 보존되지 않고, <a href="/wiki/%EC%97%B4%EC%97%AD%ED%95%99_%EC%A0%9C2%EB%B2%95%EC%B9%99" title="열역학 제2법칙">열역학 제2법칙</a>에 따라 시간에 따라 증가한다. <a href="/wiki/%EB%8F%85%EC%9D%BC" title="독일">독일</a>의 물리학자 <a href="/wiki/%EB%A3%A8%EB%8F%8C%ED%94%84_%ED%81%B4%EB%9D%BC%EC%9A%B0%EC%A7%80%EC%9A%B0%EC%8A%A4" title="루돌프 클라우지우스">루돌프 클라우지우스</a>가 1850년대 초에 도입하였다. 대개 기호로 라틴 대문자 <i>S</i>를 쓴다. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="정의"><span id=".EC.A0.95.EC.9D.98"></span>정의</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=1" title="부분 편집: 정의"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>엔트로피에는 열역학적 정의와 통계학적인 정의, 두 가지의 관련된 정의가 있다. 역사적으로, 고전 열역학적 정의가 먼저 발전하였다. 고전 열역학적인 관점에서, 그 이론은 원자나 분자 같은 수많은 성분들로 이루어져 있고, 학설의 안정성은 그러한 성분들의 평균적인 열특성으로 설명된다. 이론을 구성하는 성분의 세부적인 성분들은 직접적으로 보이지 않는다. 그러나 그 특성은 <a href="/wiki/%EC%98%A8%EB%8F%84" title="온도">온도</a>, <a href="/wiki/%EC%95%95%EB%A0%A5" title="압력">압력</a>, 엔트로피, <a href="/wiki/%EC%97%B4%EC%9A%A9%EB%9F%89" title="열용량">열용량</a>과 같은 눈으로 볼 수 있는 평균적인 지표들에 의해 설명된다. 그 이론의 특성에 관한 고전적인 정의는 평형 상태임을 가정하였다. 엔트로피의 고전 열역학적 정의는 최근 비평형 열역학의 영역으로까지 확대되었다. 이후 엔트로피를 포함한 열특성은 눈으로 볼 수 없는 미시세계에서의 움직임에 대한 정역학적인 관점에서 새롭게 정의되었다. 그 예로 처음에는 기체로 여겨졌지만 시간이 지난 후에 <a href="/wiki/%EA%B4%91%EC%9E%90" title="광자">광자</a>, 음자, 스핀과 같은 양자 역학적으로 생각되는 뉴턴 입자가 있다. 이 이론의 특성에 대한 통계학적 설명은 고전적인 열역학을 사용하여 이론의 특성을 정의하는 것이 몇몇 변수의 영향을 받는 이론의 최종적인 상태를 예측하는데 있어서 점점 신뢰할 수 없는 예측 기술이 되어감으로 인하여 필수적인 것이 되었다. </p> <div class="mw-heading mw-heading3"><h3 id="열역학적_정의"><span id=".EC.97.B4.EC.97.AD.ED.95.99.EC.A0.81_.EC.A0.95.EC.9D.98"></span>열역학적 정의</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=2" title="부분 편집: 열역학적 정의"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>고전적 열역학에서는 엔트로피 <i>S</i>의 절대적 값은 정의할 수 없고, 대신 그 상대적 변화만 정의한다.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>주 1<span class="cite-bracket">]</span></a></sup> 열적 평형을 이뤄 온도가 <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 T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>인 계에 열 <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 \delta Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf715eece146c816847a8c5d56eae97798453d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.887ex; height:2.676ex;" alt="{\displaystyle \delta Q}"></span>를 가하였다고 하자.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>주 2<span class="cite-bracket">]</span></a></sup> 이 경우 엔트로피의 증가는 다음과 같이 정의한다. </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 dS=\delta Q/T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>S</mi> <mo>=</mo> <mi>δ</mi> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dS=\delta Q/T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed3aeb0796f6558cabc00683e2734e81cea687a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.499ex; height:2.843ex;" alt="{\displaystyle dS=\delta Q/T}"></span>.</dd></dl> <p>이 식을 적분하여 유한한 엔트로피 차이를 정의한다. </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 \Delta S=\int {\frac {\delta Q}{T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>S</mi> <mo>=</mo> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>Q</mi> </mrow> <mi>T</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta S=\int {\frac {\delta Q}{T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/150f4ed7f11c45dd56a9724c0810c49cb83c160e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.837ex; height:5.843ex;" alt="{\displaystyle \Delta S=\int {\frac {\delta Q}{T}}}"></span>.</dd></dl> <p>엔트로피는 온도의 함수로써, 주어진 열이 일로 전환될 수 있는 가능성을 나타낸다. 예를 들어 같은 크기의 열량이라도 고온의 계에 더해졌을 때보다 저온의 계에 더해졌을 경우에 계의 엔트로피가 크게 증가한다. 따라서 엔트로피가 최대일 때 열에너지가 일로 전환될 수 있는 가능성은 최소이고, 반대로 엔트로피가 최소일 때 열에너지가 일로 전환될 수 있는 가능성이 최대가 된다. 실제로 외부적인 일을 할 수 있는 <a href="/wiki/%EC%97%90%EB%84%88%EC%A7%80" title="에너지">에너지</a>를 "유용한 에너지", 존재하지만 외부적인 일을 하는 데에 쓰일 수 없는 에너지를 "사용불가능한 에너지"라고 한다. 계의 총 에너지를 "유용한 에너지"와 "사용불가능한 에너지"의 합으로 정의 할 때, 엔트로피는 전체 에너지에서 차지하는 비율이 주어진 계의 절대 온도에 반비례하는 "사용불가능한 에너지"의 일종으로 볼 수 있다. <a href="/wiki/%EA%B9%81%EC%8A%A4_%EC%9E%90%EC%9C%A0_%EC%97%90%EB%84%88%EC%A7%80" title="깁스 자유 에너지">깁스 자유 에너지</a> 또는 <a href="/wiki/%ED%97%AC%EB%A6%84%ED%99%80%EC%B8%A0_%EC%9E%90%EC%9C%A0_%EC%97%90%EB%84%88%EC%A7%80" title="헬름홀츠 자유 에너지">헬름홀츠 자유 에너지</a>와의 관계식에서 "TS" 로 나타나는 것을 생각해 보라. </p><p>엔트로피는 계의 <a href="/wiki/%EC%9E%90%EC%9C%A0_%EC%97%90%EB%84%88%EC%A7%80" class="mw-disambig" title="자유 에너지">자유 에너지</a>를 결정짓는 요소 가운데 하나이다. 온도는 평형 상태에 있는 계에서만 정의되는 값이므로, 이와 같은 엔트로피의 열역학적인 정의는 오직 평형 상태에 있는 계에서만 성립한다. 반면 통계역학적인 엔트로피의 정의는 모든 계에 적용된다 (아래 참고). 따라서 엔트로피의 보다 근본적인 정의로는 통계역학적인 정의를 꼽을 수 있다. 엔트로피의 증가는 흔히 분자들의 무질서도의 증가<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>로 정의되어 왔으며, 최근들어 엔트로피는 에너지의 "<a href="/wiki/%EB%B6%84%EC%82%B0" title="분산">분산</a>"으로 해석되고 있다. </p> <div class="mw-heading mw-heading3"><h3 id="통계역학적_정의"><span id=".ED.86.B5.EA.B3.84.EC.97.AD.ED.95.99.EC.A0.81_.EC.A0.95.EC.9D.98"></span>통계역학적 정의</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=3" title="부분 편집: 통계역학적 정의"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>통계역학에서는 엔트로피의 차 뿐만 아니라 엔트로피의 절대적 값을 정의할 수 있다. 확률적 상태 분포를 가지는 어떤 계의 <a href="/wiki/%EC%95%99%EC%83%81%EB%B8%94_(%EB%AC%BC%EB%A6%AC%ED%95%99)" title="앙상블 (물리학)">앙상블</a>을 생각하자. 여기서 단일계의 상태(미시적 상태) <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>의 확률을 <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 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></span><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}}"></span>라고 하자. 이 경우, 앙상블의 엔트로피는 다음과 같이 정의한다. </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 S=-k_{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"> <mi>B</mi> </mrow> </msub> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=-k_{B}\sum _{i}p_{i}\ln p_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45a5b959edf49a7de8f2965318b11c3c4b7b38b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:19.878ex; height:5.509ex;" alt="{\displaystyle S=-k_{B}\sum _{i}p_{i}\ln p_{i}}"></span></dd></dl> <p>고립된 계의 경우, 통상적으로 모든 미시적 상태의 확률이 같다고 가정한다. 즉 <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 p_{i}=1/\Omega }"> <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> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}=1/\Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21a80eb8fc6253da3d56f231ab5f2578de98a926" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:9.16ex; height:2.843ex;" alt="{\displaystyle p_{i}=1/\Omega }"></span> (여기서 <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 \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Omega }"></span>는 가능한 미시적 상태의 수)다. 이 경우 </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 S=k_{B}\ln \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡</mo> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=k_{B}\ln \Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e401c5acab7d5886826a0ac20e3da7487b72311" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.68ex; height:2.509ex;" alt="{\displaystyle S=k_{B}\ln \Omega }"></span></dd></dl> <p>다. 여기서 <i>k</i><sub>B</sub>는 <a href="/wiki/%EB%B3%BC%EC%B8%A0%EB%A7%8C_%EC%83%81%EC%88%98" title="볼츠만 상수">볼츠만 상수</a>다. 이 식은 <a href="/wiki/%EB%A3%A8%ED%8A%B8%EB%B9%84%ED%9E%88_%EB%B3%BC%EC%B8%A0%EB%A7%8C" title="루트비히 볼츠만">루트비히 볼츠만</a>이 처음 발견하였다. </p><p><a href="/wiki/%EC%97%B4%EC%9B%90" title="열원">열저장고</a>와 열적 평형을 이룬 계의 미시상태는 <a href="/wiki/%EB%B3%BC%EC%B8%A0%EB%A7%8C_%EB%B6%84%ED%8F%AC" title="볼츠만 분포">볼츠만 분포</a> <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 p_{i}\propto \exp(-E_{i}/k_{B}T)}"> <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> <mo>∝</mo> <mi>exp</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}\propto \exp(-E_{i}/k_{B}T)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd04509bf1011f11b1ffe4501fad5ca88f6dbdeb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:20.331ex; height:2.843ex;" alt="{\displaystyle p_{i}\propto \exp(-E_{i}/k_{B}T)}"></span>를 따른다. 이 경우 엔트로피는 다음과 같다. </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 S=k_{B}{\frac {\partial }{\partial T}}(T\ln Z(T))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mi>ln</mi> <mo>⁡</mo> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=k_{B}{\frac {\partial }{\partial T}}(T\ln Z(T))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae391a7adf76dffd9f35c61d8aca5540378f7057" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:22.364ex; height:5.509ex;" alt="{\displaystyle S=k_{B}{\frac {\partial }{\partial T}}(T\ln Z(T))}"></span></dd></dl> <p>여기서 <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 Z(T)=\sum _{i}\exp(-E_{i}/k_{B}T)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <mi>exp</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z(T)=\sum _{i}\exp(-E_{i}/k_{B}T)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1eda28ef6bdbccf9bdfff3435b1719aca220dfd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:27.141ex; height:5.509ex;" alt="{\displaystyle Z(T)=\sum _{i}\exp(-E_{i}/k_{B}T)}"></span>는 <a href="/wiki/%EB%B6%84%EB%B0%B0%ED%95%A8%EC%88%98" class="mw-redirect mw-disambig" title="분배함수">분배함수</a>다. <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=-k_{B}T\ln Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <mi>ln</mi> <mo>⁡</mo> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=-k_{B}T\ln Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13a2916f276c5612a75b32d742cd100b19ce6135" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.371ex; height:2.509ex;" alt="{\displaystyle A=-k_{B}T\ln Z}"></span>를 <a href="/wiki/%ED%97%AC%EB%A6%84%ED%99%80%EC%B8%A0_%EC%9E%90%EC%9C%A0_%EC%97%90%EB%84%88%EC%A7%80" title="헬름홀츠 자유 에너지">헬름홀츠 자유 에너지</a>로 정의하여, <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 S=-\partial A/\partial T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∂</mi> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=-\partial A/\partial T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e150eda32daff8d3656757f081d7a3515c9601a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.584ex; height:2.843ex;" alt="{\displaystyle S=-\partial A/\partial T}"></span>로 쓰기도 한다. </p> <div class="mw-heading mw-heading3"><h3 id="양자역학적_정의"><span id=".EC.96.91.EC.9E.90.EC.97.AD.ED.95.99.EC.A0.81_.EC.A0.95.EC.9D.98"></span>양자역학적 정의</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=4" title="부분 편집: 양자역학적 정의"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>양자역학적 앙상블은 <a href="/wiki/%EB%B0%80%EB%8F%84%ED%96%89%EB%A0%AC" class="mw-redirect" title="밀도행렬">밀도행렬</a> <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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>로 나타내어진다. 이 경우, <b>폰노이만 엔트로피</b>(<span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">von Neumann entropy</span>)를 다음과 같이 정의한다. </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 S=-k_{B}\operatorname {tr} (\rho \ln \rho )}"> <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"> <mi>B</mi> </mrow> </msub> <mi>tr</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ρ</mi> <mi>ln</mi> <mo>⁡</mo> <mi>ρ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=-k_{B}\operatorname {tr} (\rho \ln \rho )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94081a05ed255c72342e00b7e73ceae225d6d216" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.227ex; height:2.843ex;" alt="{\displaystyle S=-k_{B}\operatorname {tr} (\rho \ln \rho )}"></span></dd></dl> <p>밀도행렬을 대각화하면 그 각 원소는 확률 <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 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></span><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}}"></span>가 되므로, 이는 위의 통계역학적 정의와 동등하다. 이 정의는 <a href="/wiki/%EC%A1%B4_%ED%8F%B0_%EB%85%B8%EC%9D%B4%EB%A7%8C" title="존 폰 노이만">존 폰 노이만</a>이 발견하였다. </p> <div class="mw-heading mw-heading3"><h3 id="블랙홀의_엔트로피"><span id=".EB.B8.94.EB.9E.99.ED.99.80.EC.9D.98_.EC.97.94.ED.8A.B8.EB.A1.9C.ED.94.BC"></span>블랙홀의 엔트로피</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=5" title="부분 편집: 블랙홀의 엔트로피"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r34311305">.mw-parser-output .hatnote{}.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}</style><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/18px-Icons8_flat_search.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/27px-Icons8_flat_search.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/36px-Icons8_flat_search.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span> 이 부분의 본문은 <a href="/wiki/%EB%B8%94%EB%9E%99%ED%99%80_%EC%97%B4%EC%97%AD%ED%95%99" title="블랙홀 열역학">블랙홀 열역학</a>입니다.</div> <p><a href="/wiki/%EB%B8%94%EB%9E%99%ED%99%80" title="블랙홀">블랙홀</a>은 고전적으로 <a href="/wiki/%ED%84%B8%EC%97%86%EC%9D%8C_%EC%A0%95%EB%A6%AC" title="털없음 정리">털없음 정리</a>에 의하여 미시상태가 없다. 그러나 반고전으로 마치 어떤 유한한 엔트로피를 가진 것처럼 행동한다. 이 엔트로피는 </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 S={\frac {k_{B}c^{3}}{4G\hbar }}\cdot A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> <mi>G</mi> <mi class="MJX-variant">ℏ</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S={\frac {k_{B}c^{3}}{4G\hbar }}\cdot A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b172ea9bbeb91a17ac20fd0aafbe79b7f965bf1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.608ex; height:5.843ex;" alt="{\displaystyle S={\frac {k_{B}c^{3}}{4G\hbar }}\cdot A}"></span></dd></dl> <p>다. 여기서 <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>는 블랙홀의 <a href="/wiki/%EC%82%AC%EA%B1%B4_%EC%A7%80%ED%8F%89%EC%84%A0" class="mw-redirect" title="사건 지평선">사건 지평선</a>의 넓이다. 이를 <b><a href="/wiki/%EB%B2%A0%EC%BC%84%EC%8A%88%ED%83%80%EC%9D%B8-%ED%98%B8%ED%82%B9_%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC" class="mw-redirect" title="베켄슈타인-호킹 엔트로피">베켄슈타인-호킹 엔트로피</a></b>(<span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">Bekenstein–Hawking entropy</span>)라고 부른다. 이는 야콥 베켄슈타인(<span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">Jacob Bekenstein</span>, <span style="font-size: smaller;"><a href="/wiki/%ED%9E%88%EB%B8%8C%EB%A6%AC%EC%96%B4" title="히브리어">히브리어</a>: </span><span lang="he">יעקב בקנשטיין</span>)이 가설을 세웠고, <a href="/wiki/%EC%8A%A4%ED%8B%B0%EB%B8%90_%ED%98%B8%ED%82%B9" title="스티븐 호킹">스티븐 호킹</a>이 반고전적으로 유도하였다. 또한, 특수한 경우 <a href="/wiki/%EB%81%88_%EC%9D%B4%EB%A1%A0" title="끈 이론">끈 이론</a>이나 <a href="/wiki/%EB%A3%A8%ED%94%84_%EC%96%91%EC%9E%90_%EC%A4%91%EB%A0%A5" class="mw-redirect" title="루프 양자 중력">루프 양자 중력</a> 등으로 미시적으로 유도할 수도 있다. 블랙홀을 포함하는 계의 경우, 베켄슈타인-호킹 엔트로피를 무시하고 계산하면 일반적으로 열역학 제2법칙이 성립하지 않고, 이를 포함하여 계산하여야만 성립한다. </p> <div class="mw-heading mw-heading2"><h2 id="성질"><span id=".EC.84.B1.EC.A7.88"></span>성질</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=6" title="부분 편집: 성질"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><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 ST_{R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ST_{R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef2166f4de6f2e50b5e6c68bcf62e3b51a7ec0a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.336ex; height:2.509ex;" alt="{\displaystyle ST_{R}}"></span>은 특정 <a href="/wiki/%EC%98%A8%EB%8F%84" title="온도">온도</a> <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 T_{R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7160eae5d90dbb2b5d8df9743c9274a5062d2924" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.837ex; height:2.509ex;" alt="{\displaystyle T_{R}}"></span>에서 시스템의 에너지 중에서 <a href="/wiki/%EC%9D%BC_(%EB%AC%BC%EB%A6%AC)" class="mw-redirect" title="일 (물리)">일</a>로 변환할 수 없는 에너지를 나타낸다. 따라서 전체 에너지에서 <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 ST_{R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ST_{R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef2166f4de6f2e50b5e6c68bcf62e3b51a7ec0a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.336ex; height:2.509ex;" alt="{\displaystyle ST_{R}}"></span>을 뺀 양이 <a href="/wiki/%EC%9E%90%EC%9C%A0_%EC%97%90%EB%84%88%EC%A7%80" class="mw-disambig" title="자유 에너지">자유 에너지</a>가 된다. </p> <div class="mw-heading mw-heading2"><h2 id="열_엔트로피와_위치_엔트로피"><span id=".EC.97.B4_.EC.97.94.ED.8A.B8.EB.A1.9C.ED.94.BC.EC.99.80_.EC.9C.84.EC.B9.98_.EC.97.94.ED.8A.B8.EB.A1.9C.ED.94.BC"></span>열 엔트로피와 위치 엔트로피</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=7" title="부분 편집: 열 엔트로피와 위치 엔트로피"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>엔트로피란 우주 내부 어떤 시스템에서 생기는 유용한 에너지가 무용한 에너지로 변화하는 량의 척도이다. 엔트로피를 계를 구성하는 성분들의 배열의 관점에서 바라보게 된다면, 위치 엔트로피와 열 엔트로피로 분류할 수 있다. 여기서 열 엔트로피는 분자들 사이에서의 에너지 양자의 분포들에 의한 구별가능한 배열을 기준으로 하여 계산된 엔트로피를 말한다. </p><p>위와 같이 분류한 엔트로피를 계의 관점에서 본 알짜엔트로피 변화를 나타낼 때 이용할 수 있다. </p><p>계와 주위가 갖는 엔트로피는 다음과 같이 표현할 수 있다 </p><p><b><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 \Delta S_{net}=\Delta S_{system}+\Delta S_{surrounding}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>y</mi> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>m</mi> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>u</mi> <mi>r</mi> <mi>r</mi> <mi>o</mi> <mi>u</mi> <mi>n</mi> <mi>d</mi> <mi>i</mi> <mi>n</mi> <mi>g</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta S_{net}=\Delta S_{system}+\Delta S_{surrounding}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/416c5e42314ec3c6744a6dd391ba52de99cd77c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:33.346ex; height:2.843ex;" alt="{\displaystyle \Delta S_{net}=\Delta S_{system}+\Delta S_{surrounding}}"></span></b> </p><p>여기서 열 엔트로피는 계와 주위 모두에 존재하지만, 계를 제외한 모든 곳을 지칭하는 주위에서 위치 엔트로피의 변화는 너무 광범위하게 이루어지므로 그 변화를 무시할 수 있고, 주위가 갖는 엔트로피 변화에 가장 큰 영향을 미치는 것은 온도, 즉 열 엔트로피이다. 이 때문에 주위의 엔트로피 변화를 열 엔트로피 변화라고 할 수 있다. 그리고 이와 같은 관점에서 계에서 열 엔트로피변화는 분명 존재하긴 하지만 위치 엔트로피의 변화가 더욱 계의 엔트로피변화에 큰 영향을 주기 때문에 계의 엔트로피 변화를 위치 엔트로피의 변화라 할 수 있다. </p> <div class="mw-heading mw-heading2"><h2 id="엔트로피에_관한_작품"><span id=".EC.97.94.ED.8A.B8.EB.A1.9C.ED.94.BC.EC.97.90_.EA.B4.80.ED.95.9C_.EC.9E.91.ED.92.88"></span>엔트로피에 관한 작품</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=8" title="부분 편집: 엔트로피에 관한 작품"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%EC%95%84%EC%9D%B4%EC%9E%91_%EC%95%84%EC%8B%9C%EB%AA%A8%ED%94%84" title="아이작 아시모프">아이작 아시모프</a>의 단편 소설 《<a href="/wiki/%EC%B5%9C%ED%9B%84%EC%9D%98_%EC%A7%88%EB%AC%B8" title="최후의 질문">최후의 질문</a>》.</li> <li><a href="/wiki/%EC%A0%9C%EB%A0%88%EB%AF%B8_%EB%A6%AC%ED%94%84%ED%82%A8" class="mw-redirect" title="제레미 리프킨">제레미 리프킨</a>의 책 《엔트로피》. 비록 자연과학적 시선과는 일치하지 않으나 엔트로피 법칙을 사회학적으로 해석하였다. 만물은 유용에서 무용으로의 한가지 방향으로만 흐르며 결국에는 세계는 무질서에 휩싸일 것이라고 경고하며 새로운 세계관을 역설하고 있다. [Rifkin, Jeremy, and Ted Howard. Entropy: A New World View. New York: Viking, 1980. Print.]</li></ul> <div class="mw-heading mw-heading2"><h2 id="같이_보기"><span id=".EA.B0.99.EC.9D.B4_.EB.B3.B4.EA.B8.B0"></span>같이 보기</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=9" title="부분 편집: 같이 보기"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> 위키미디어 공용에 <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Entropy?uselang=ko">엔트로피</a></span> 관련 미디어 분류가 있습니다.</li> <li><a href="/wiki/%ED%98%BC%EB%8F%88_%EC%9D%B4%EB%A1%A0" title="혼돈 이론">혼돈 이론</a></li> <li><a href="/wiki/%EB%A7%A5%EC%8A%A4%EC%9B%B0%EC%9D%98_%EB%8F%84%EA%B9%A8%EB%B9%84" title="맥스웰의 도깨비">맥스웰의 도깨비</a></li> <li><a href="/wiki/%EC%8A%A4%ED%84%B8%EB%A7%81_%EA%B7%BC%EC%82%AC" title="스털링 근사">스털링 근사</a></li> <li><a href="/wiki/%EA%B8%B0%EB%B8%8C%EC%8A%A4_%EC%9E%90%EC%9C%A0_%EC%97%90%EB%84%88%EC%A7%80" class="mw-redirect" title="기브스 자유 에너지">기브스 자유 에너지</a></li> <li><a href="/w/index.php?title=%EC%9E%94%EC%97%AC_%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&redlink=1" class="new" title="잔여 엔트로피 (없는 문서)">잔여 엔트로피</a></li> <li><a href="/wiki/%EC%A0%95%EB%B3%B4_%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC" title="정보 엔트로피">정보 엔트로피</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="주해"><span id=".EC.A3.BC.ED.95.B4"></span>주해</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=10" title="부분 편집: 주해"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r35556958">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.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"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">이는 비상대론적 고전역학에서 에너지의 절대적 값 대신 에너지의 차이만을 쓰는 것과 유사하다.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">열을 가하는 과정은 가역적일 수도, 비가역적일 수도 있다. 두 경우 모두, 열은 거시적인 일 (<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 P\;dV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P\;dV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49e14764e6c7932c1e332633b0bad96d8722441e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.394ex; height:2.176ex;" alt="{\displaystyle P\;dV}"></span>)을 제외한 모든 에너지 이동이다.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="각주"><span id=".EA.B0.81.EC.A3.BC"></span>각주</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=11" title="부분 편집: 각주"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r35556958"><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><cite class="citation book">로널드 L. 넘버스 (2016). 《창조론자들》. 새물결플러스. 378쪽. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/9791186409558" title="특수:책찾기/9791186409558"><bdi>9791186409558</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%EC%B0%BD%EC%A1%B0%EB%A1%A0%EC%9E%90%EB%93%A4&rft.pages=378&rft.pub=%EC%83%88%EB%AC%BC%EA%B2%B0%ED%94%8C%EB%9F%AC%EC%8A%A4&rft.date=2016&rft.isbn=9791186409558&rft.au=%EB%A1%9C%EB%84%90%EB%93%9C+L.+%EB%84%98%EB%B2%84%EC%8A%A4&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="외부_링크"><span id=".EC.99.B8.EB.B6.80_.EB.A7.81.ED.81.AC"></span>외부 링크</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%97%94%ED%8A%B8%EB%A1%9C%ED%94%BC&action=edit&section=12" title="부분 편집: 외부 링크"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> 위키미디어 공용에 <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Entropy?uselang=ko">엔트로피</a></span> 관련 미디어 분류가 있습니다.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140203062728/http://science.postech.ac.kr/hs/C18/C18S005.html">Postech - 과학사개론 > 엔트로피 개념에 대한 이해</a>, 저자 - 임경순</li> <li><a rel="nofollow" class="external text" href="http://navercast.naver.com/science/physics/93">네이버 캐스트 - 엔트로피는 증가한다</a>, <a rel="nofollow" class="external text" href="http://navercast.naver.com/science/physics/2184">엔트로피 증가의 법칙</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r36480591">.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 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