Mathematical problems in nonequilibrium statistical mechanics

We will discuss the weak convergence of solutions of the kinetic Liouville equation. The “fine” Gibbs entropy is constant as a function of time. But after some coarsening, the Gibbs entropy starts to change. We will discuss the conditions when the coarse-grained entropy increases as a functions of time. These questions are connected closely with the well-known problem of non-reversibility behavior (in statistical sence) of reversible dynamical systems.