  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 $\ddot{S}\ge 0$.

Statistical Mechanics