Statistical physics of frictional grains: Some simple applications of the 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 use three simple models to illustrate some of the key concepts of the statistical physics introduced by Edwards and co-workers more than 30 years ago to describe shaken granular piles: non-interacting frictional grains attached to a wall by a spring, a chain of frictional grains connected by springs, and a simplified mean-field model of a granular packing. We observe that a chain of frictional grains connected by springs exhibits a critical point at an infinite effective temperature (i.e., infinitely strong shaking) at odds with the zero-temperature critical point generically found in one-dimensional systems at thermal equilibrium in the presence of local interactions. Since the late 20th century, granular materials have been recognized as forming a distinct state of matter, neither solid nor liquid, but amenable to a statistical description. It turns out that dissipation, through inter-grain friction, governs the large-scale properties of these systems, so that the usual Boltzmann–Gibbs statistics is replaced by the Edwards statistics. These statistics are full of surprises. For instance, model granular systems can exhibit a critical point at infinite-temperature. To know more, you can delve into this paper, which can be used in advanced statistical physics courses, or as a graduate-level introduction to soft matter. [ABSTRACT FROM AUTHOR]