对洛施托帕的另一种探讨
Yet Another Approach to Loschmidt's Paradox
摘要：
Lev Petrovich Pitaevskii的作品是选择有趣研究主题的参考点。一个例子是文章[物理。第54卷，第625 -632页，2011] https://doi.org/10.3367/UFNe.0181.201106d.0647，其促进非平衡统计物理学中的严格结果。本文严格证明了非平衡态平均是局部熵极小。这种说法对应于统计力学的“熵增长”，并且不违反微观运动的时间反演对称性：熵的一阶时间导数为零$\dot{S}=0$，而二阶导数是非负的$\ddot{S}\ge 0$。
英文摘要：
The works by Lev Petrovich Pitaevskii are reference points for choosing an interesting research topic. An example is the article [Phys. Usp. Vol.54, pp.625-632, 2011] https://doi.org/10.3367/UFNe.0181.201106d.0647 which promotes rigorous results in non-equilibrium statistical physics. In present paper, we rigorously prove that a non-equilibrium state, on the average, is a local entropy minimum. This statement corresponds to the "entropy growth" of statistical mechanics and does not violate time reversal symmetry of microscopic motion: the first-order time derivative of the entropy is zero $\dot{S}=0$, while the second order derivative is non-negative $\ddot{S}\ge 0$.
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