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arXiv · 1801.08768

Yet Another Approach to Loschmidt's Paradox

Lev A. Melnikovsky
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Abstract

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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Lev A. Melnikovsky. 2018-11-12. Yet Another Approach to Loschmidt's Paradox. https://doi.org/10.1134/s1063776118110079

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