Thermodynamics and statistical mechanics of frozen systems in inherent states.

We discuss a statistical mechanics approach in the manner of Edwards to the "inherent states" (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity the inherent states are distributed according a generalized Gibbs measure obtained assuming the validity of the principle of maximum entropy, under suitable constraints. In particular, we consider three lattice models (a diluted spin glass, a monodisperse hard-sphere system under gravity, and a hard-sphere binary mixture under gravity) undergoing a schematic "tap dynamics," showing via Monte Carlo calculations that the time averages of macroscopic quantities over the tap dynamics and over such a generalized distribution coincide. We also discuss about the general validity of this approach to nonthermal systems.