  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.
