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We discuss the statistical mechanics of granular matter and derive severalsignificant results. First, we show that, contrary to common belief, the volumeand stress ensembles are inter-dependent, necessitating the use of both. We usethe combined ensemble to calculate explicitly expectation values of structuraland stress-related quantities for two-dimensional systems. We thencedemonstrate that structural properties may depend on the angoricity tensor andthat stress-based quantities may depend on the compactivity. This calls intoquestion previous statistical mechanical analyses of static granular systemsand related derivations of expectation values. Second, we establish theexistence of an intriguing equipartition principle - the total volume is sharedequally amongst both structural and stress-related degrees of freedom. Third,we derive an expression for the compactivity that makes it possible to quantifyit from macroscopic measurements.

Inter-dependence of the volume and stress ensembles and equipartition in statistical mechanics of granular systems