The Fokker–Planck equation for the translational modes of an inelastic system of Brownian particles in a non-equilibrium bath of light particles is derived from first principles of statistical mechanics. The bath and internal modes relax on a time scale that is much shorter than that of the...

The Fokker-Planck equation of a system of several Brownian particles immersed in a non-equilibrium bath of light particles is derived from first principles of statistical mechanics using time-dependent projection operators. The Fokker-Planck equation contains the usual equilibrium streaming and...