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在玻尔兹曼的定义中，熵是热力学平衡系统中可能的微观状态（或多个微观状态）数量的量度。与玻耳兹曼定义一致，热力学第二定律需要重新措词，以使熵随着时间的推移而增加，尽管基本原理保持不变。

在玻尔兹曼的定义中，熵是热力学平衡系统中可能的微观状态（或多个微观状态）数量的量度。与玻耳兹曼定义一致，热力学第二定律需要重新措词，以使熵随着时间的推移而增加，尽管基本原理保持不变。

===有序和无序===机或混乱程度相关联在一起。熵的传统定性描述是，它是指系统状态的变化，是对“分子无序”的一种度量，是动态能量从一种状态或一种状态转换为另一种状态时所浪费的能量的量。在这个方向上，最近的几位作者已经得出了精确的熵公式，以解释和测量原子和分子组分中的无序和有序。<ref name="Brooks">{{cite book|last1=Brooks|first1=Daniel R.|last2=Wiley|first2=E. O.|title=Evolution as entropy : toward a unified theory of biology|date=1988|publisher=University of Chicago Press|location=Chicago [etc.]|isbn=978-0-226-07574-7|edition=2nd}}</ref><ref name="Landsberg-A">{{cite journal | last1 = Landsberg | first1 = P.T. | year = 1984 | title = Is Equilibrium always an Entropy Maximum? | url = | journal = J. Stat. Physics | volume = 35 | issue = 1–2| pages = 159–169 | doi=10.1007/bf01017372|bibcode = 1984JSP....35..159L }}</ref><ref name="Landsberg-B">{{cite journal | last1 = Landsberg | first1 = P.T. | year = 1984 | title = Can Entropy and "Order" Increase Together? | url = | journal = Physics Letters | volume = 102A | issue = 4| pages = 171–173 | doi=10.1016/0375-9601(84)90934-4|bibcode = 1984PhLA..102..171L }}</ref>较简单的熵序/无序公式之一是热力学物理学家Peter Landsberg于1984年基于[https://en.wikipedia.org/wiki/Thermodynamics 热力学]和[https://en.wikipedia.org/wiki/Information_theory 信息理论]的结合得出的。他认为，当约束在系统上运行时，与禁止状态相比，阻止其进入可能或允许的状态中的一个或多个状态，系统中“无序”总量的度量为：<ref name="Brooks">{{cite book|last1=Brooks|first1=Daniel R.|last2=Wiley|first2=E. O.|title=Evolution as entropy : toward a unified theory of biology|date=1988|publisher=University of Chicago Press|location=Chicago [etc.]|isbn=978-0-226-07574-7|edition=2nd}}</ref><ref name="Landsberg-A">{{cite journal | last1 = Landsberg | first1 = P.T. | year = 1984 | title = Is Equilibrium always an Entropy Maximum? | url = | journal = J. Stat. Physics | volume = 35 | issue = 1–2| pages = 159–169 | doi=10.1007/bf01017372|bibcode = 1984JSP....35..159L }}</ref><ref name="Landsberg-B">{{cite journal | last1 = Landsberg | first1 = P.T. | year = 1984 | title = Can Entropy and "Order" Increase Together? | url = | journal = Physics Letters | volume = 102A | issue = 4| pages = 171–173 | doi=10.1016/0375-9601(84)90934-4|bibcode = 1984PhLA..102..171L }}</ref>

===有序和无序===

熵通常与有序、无序或混乱程度相关联在一起。熵的传统定性描述是，它是指系统状态的变化，是对“分子无序”的一种度量，是动态能量从一种状态或一种状态转换为另一种状态时所浪费的能量的量。在这个方向上，最近的几位作者已经得出了精确的熵公式，以解释和测量原子和分子组分中的无序和有序。<ref name="Brooks">{{cite book|last1=Brooks|first1=Daniel R.|last2=Wiley|first2=E. O.|title=Evolution as entropy : toward a unified theory of biology|date=1988|publisher=University of Chicago Press|location=Chicago [etc.]|isbn=978-0-226-07574-7|edition=2nd}}</ref><ref name="Landsberg-A">{{cite journal | last1 = Landsberg | first1 = P.T. | year = 1984 | title = Is Equilibrium always an Entropy Maximum? | url = | journal = J. Stat. Physics | volume = 35 | issue = 1–2| pages = 159–169 | doi=10.1007/bf01017372|bibcode = 1984JSP....35..159L }}</ref><ref name="Landsberg-B">{{cite journal | last1 = Landsberg | first1 = P.T. | year = 1984 | title = Can Entropy and "Order" Increase Together? | url = | journal = Physics Letters | volume = 102A | issue = 4| pages = 171–173 | doi=10.1016/0375-9601(84)90934-4|bibcode = 1984PhLA..102..171L }}</ref>较简单的熵序/无序公式之一是热力学物理学家Peter Landsberg于1984年基于[https://en.wikipedia.org/wiki/Thermodynamics 热力学]和[https://en.wikipedia.org/wiki/Information_theory 信息理论]的结合得出的。他认为，当约束在系统上运行时，与禁止状态相比，阻止其进入可能或允许的状态中的一个或多个状态，系统中“无序”总量的度量为：<ref name="Brooks">{{cite book|last1=Brooks|first1=Daniel R.|last2=Wiley|first2=E. O.|title=Evolution as entropy : toward a unified theory of biology|date=1988|publisher=University of Chicago Press|location=Chicago [etc.]|isbn=978-0-226-07574-7|edition=2nd}}</ref><ref name="Landsberg-A">{{cite journal | last1 = Landsberg | first1 = P.T. | year = 1984 | title = Is Equilibrium always an Entropy Maximum? | url = | journal = J. Stat. Physics | volume = 35 | issue = 1–2| pages = 159–169 | doi=10.1007/bf01017372|bibcode = 1984JSP....35..159L }}</ref><ref name="Landsberg-B">{{cite journal | last1 = Landsberg | first1 = P.T. | year = 1984 | title = Can Entropy and "Order" Increase Together? | url = | journal = Physics Letters | volume = 102A | issue = 4| pages = 171–173 | doi=10.1016/0375-9601(84)90934-4|bibcode = 1984PhLA..102..171L }}</ref>

<math>Disorder={C_\text{D}\over C_\text{I}}.\,</math>

<math>Disorder={C_\text{D}\over C_\text{I}}.\,</math>