We discuss recent developments in the formulation of a Statistical Mechanics approach to non thermal systems, such as granular media. We review a few important numerical results on the assessment of Edwards' theory and, in particular, we apply these ideas to study a mean field model of a hard sphere binary mixture under gravity, which can be fully analytically investigated. As a consequence, we derive the rich phase diagram and predict the features of segregation patterns of the mixture.

Contribution to November 2002 Santa Fe workshop "Anomalous Distributions, Nonlinear Dynamics and Nonextensivity", to appear in Physica D