Why granular media are thermal after all

Abstract

Two approaches exist to account for granular behavior. The thermal one considers the total entropy, which includes microscopic degrees of freedom such as phonons; the athermal one (as with the Edward entropy) takes grains as elementary. Granular solid hydrodynamics (GSH) belongs to the first, DEM, granular kinetic theory and athermal statistical mechanics (ASM) to the second. A careful discussion of their conceptual differences is given here. Three noteworthy insights or results are: (1) While DEM and granular kinetic theory are well justified to take grains as elementary, any athermal entropic consideration is bound to run into trouble. (2) Many general principles are taken as invalid in granular media. Yet within the thermal approach, energy conservation and fluctuation-dissipation theorem remain valid, granular temperatures equilibrate, and phase space is well explored in a grain at rest. Hence these are abnormalities of the athermal approximation, not of granular media as such. (3) GSH is a wide-ranged continuum mechanical description of granular dynamics.