Yet Another Approach to Loschmidt’s Paradox

Abstract

The works by Lev Petrovich Pitaevskii are reference points for choosing an interesting research topic. An example is the article [1] which promotes rigorous results in nonequilibrium statistical physics. In present paper, we rigorously prove that a nonequilibrium 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 \(\ddot {S}\) ≥ 0.