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'''Ludwig Eduard Boltzmann''' ({{IPA-de|ˈluːtvɪg ˈbɔlt͡sman}}; February 20, 1844 – September 5, 1906) was an [[Austria]]n [[physicist]] and [[philosopher]]. His greatest achievements were the development of [[statistical mechanics]], and the statistical explanation of the [[second law of thermodynamics]]. In 1877 he provided the current definition of [[entropy]],<math>S = k_{\rm B} \ln \Omega \!</math>, interpreted as a measure of statistical disorder of a system.<ref name="EncycloBritan">{{cite book
'''Ludwig Eduard Boltzmann''' ({{IPA-de|ˈluːtvɪg ˈbɔlt͡sman}}; February 20, 1844 – September 5, 1906) was an [[Austria]]n [[physicist]] and [[philosopher]]. His greatest achievements were the development of [[statistical mechanics]], and the statistical explanation of the [[second law of thermodynamics]]. In 1877 he provided the current definition of [[entropy]], <math>S = k_{\rm B} \ln \Omega \!</math>, interpreted as a measure of statistical disorder of a system.<ref name="EncycloBritan">{{cite book
|last1= Klein
|last1= Klein
|first1= Martin
|first1= Martin
| page = 300}}</ref>
| page = 300}}</ref>
路德维希·爱德华·玻尔兹曼（1844年2月20日—1906年9月5日），奥地利物理学家、哲学家。他最伟大的功绩是发展了统计力学，并且从统计意义出发解释了热力学第二定律。1877年，他给出了目前熵的定义，即玻尔兹曼熵公式：<math><math>S = k_{\rm B} \ln \Omega \!<math></math>，将熵解释为系统统计无序性的度量<ref name="EncycloBritan">{{cite book
路德维希·爱德华·玻尔兹曼（1844年2月20日—1906年9月5日），奥地利物理学家、哲学家。他最伟大的功绩是发展了统计力学，并且从统计意义出发解释了热力学第二定律。1877年，他给出了目前熵的定义，即玻尔兹曼熵公式：<math>S = k_{\rm B} \ln \Omega \!</math>，将熵解释为系统统计无序性的度量<ref name="EncycloBritan">{{cite book
|last1= Klein
|last1= Klein
|first1= Martin
|first1= Martin
where ''i'' ranges over all possible molecular conditions, and where <math>!</math> denotes [[factorial]]. The "correction" in the denominator account for [[Identical particles|indistinguishable]] particles in the same condition.
where ''i'' ranges over all possible molecular conditions, and where <math>!</math> denotes [[factorial]]. The "correction" in the denominator account for [[Identical particles|indistinguishable]] particles in the same condition.
普朗克曾说：“熵和概率之间的对数联系是由玻尔兹曼在他的气体动力学理论中首次提出的”。也就是著名的熵公式：<math> S = k_B \ln W </math>
普朗克曾说：“熵和概率之间的对数联系是由玻尔兹曼在他的气体动力学理论中首次提出的”。也就是著名的熵公式：<math> S = k_B \ln W </math>，其中''k<sub>B</sub>'' 是玻尔兹曼常数，''W'' 代表德文中宏观状态出现的概率，更准确一些来说，是对应于系统宏观状态的可能微观状态的数量——在一个系统的(可观察的)热力学状态下的(不可观测的)“方式”的数量，可以通过分配不同的位置和动量给不同的分子来实现。玻尔兹曼的范式是N个相同粒子的理想气体，其中Ni处于第i个微观位置和动量条件(范围)。''W 可以''
Boltzmann could also be considered one of the forerunners of quantum mechanics due to his suggestion in 1877 that the energy levels of a physical system could be discrete.
Boltzmann could also be considered one of the forerunners of quantum mechanics due to his suggestion in 1877 that the energy levels of a physical system could be discrete.