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Boltzmann tried for many years to "prove" the [[second law of thermodynamics]] using his gas-dynamical equation — his famous [[H-theorem]]. However the key assumption he made in formulating the collision term was "[[molecular chaos]]", an assumption which breaks [[CPT symmetry|time-reversal symmetry]] as is necessary for ''anything'' which could imply the second law. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with [[Johann Josef Loschmidt|Loschmidt]] and others over [[Loschmidt's paradox]] ultimately ended in his failure.

Boltzmann tried for many years to "prove" the [[second law of thermodynamics]] using his gas-dynamical equation — his famous [[H-theorem]]. However the key assumption he made in formulating the collision term was "[[molecular chaos]]", an assumption which breaks [[CPT symmetry|time-reversal symmetry]] as is necessary for ''anything'' which could imply the second law. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with [[Johann Josef Loschmidt|Loschmidt]] and others over [[Loschmidt's paradox]] ultimately ended in his failure.

玻尔兹曼多年来一直试图用他的气体动力学方程——著名的“H”定理来“证明”热力学第二定律。然而，他在公式化碰撞项时所做的关键假设是“分子混沌”，该假设打破了时间反转对称性，这对于任何可能指向第二定律的内容都是必要的。玻尔兹曼表面上的成功仅仅来自概率假设，所以他与洛施密特 [[Johann Josef Loschmidt|Loschmidt]] 和其他人就洛施密特悖论的长期争论最终以他的失败告终。

玻尔兹曼多年来一直试图用他的气体动力学方程——著名的“H”定理来“证明”热力学第二定律。然而，他在公式化碰撞项时所做的关键假设是“分子混沌”，该假设打破了时间反转对称性，这对于任何可能指向第二定律的内容都是必要的。玻尔兹曼表面上的成功仅仅来自概率假设，所以他与洛施密特 [[Johann Josef Loschmidt|Loschmidt]] 和其他人就'''洛施密特悖论 [[Loschmidt's paradox]]''' 的长期争论最终以他的失败告终。

Finally, in the 1970s [[E.G.D. Cohen]] and J. R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently, [[non-equilibrium statistical mechanics|nonequilibrium statistical mechanics]] for dense gases and liquids focuses on the [[Green–Kubo relations]], the [[fluctuation theorem]], and other approaches instead.

Finally, in the 1970s [[E.G.D. Cohen]] and J. R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently, [[non-equilibrium statistical mechanics|nonequilibrium statistical mechanics]] for dense gases and liquids focuses on the [[Green–Kubo relations]], the [[fluctuation theorem]], and other approaches instead.

最后，在20世纪70年代E.G.D. Cohen和J. R. Dorfman证明了玻尔兹曼方程在高密度上的系统(幂级数)推广在数学上是不可能的。因此，稠密气体和液体的非平衡统计力学侧重于Green-Kubo关系、涨落定理和其他方法。

最后，在20世纪70年代科恩 E.G.D. Cohen和多夫曼 J. R. Dorfman证明了玻尔兹曼方程在高密度上的系统(幂级数)推广在数学上是不可能的。因此，稠密气体和液体的非平衡统计力学侧重于格林-久保亮五关系、涨落定理和其他方法。