  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.
