Statistical mechanics, kinetic theory, and hydrodynamics for rapid granular flow

A system of smooth hard spheres with inelastic collisions is considered as an idealized model to describe rapid granular flow. A non-equilibrium statistical mechanics is formulated for this system, analogous to that for elastic collisions. The associated Liouville equation provides the basis for application of many-body methods such as linear response, kinetic theory, and the derivation of macroscopic hydrodynamic equations. These methods are illustrated for the simplest case of self-diffusion. A Green-Kubo expression for the self-diffusion coefficient is derived and evaluated using an approximate linear kinetic theory. Other recent applications of kinetic theory and kinetic models are reviewed briefly.