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Statistical physics of frictional grains: some simple applications of Edwards statistics

Granular matter like sand is composed of a large number of interacting grains, and is thus expected to be amenable to a statistical physics treatment. Yet, the frictional properties of grains make the statistical physics of granular matter significantly different from the equilibrium statistical physics of atomic or molecular systems. We illustrate here on simple models some of the key concepts of the statistical physics introduced by Edwards and coworkers more than thirty years ago to describe shaken granular piles. Quite surprisingly, properties of such frictional systems observed at high effective temperature (i.e., strong shaking) may share some analogies with some low temperature properties of equilibrium systems. For instance, the effective specific heat of non-interacting frictional grains under strong shaking in a harmonic potential goes to zero in the high temperature limit. As a second example, a chain of frictional grains linked by springs exhibits a critical point at infinite effective temperature, at odds with the zero-temperature critical point generically found in one-dimensional equilibrium systems in the presence of local interactions.