Interdependence of the volume and stress ensembles and equipartition in statistical mechanics of granular systems.
We discuss the statistical mechanics of granular matter and derive several significant results. First, we show that, contrary to common belief, the volume and stress ensembles are interdependent, necessitating the use of both. We use the combined ensemble to calculate explicitly expectation values of structural and stress-related quantities for two-dimensional systems. We thence demonstrate that structural properties may depend on the angoricity tensor and that stress-based quantities may depend on the compactivity. This calls into question previous statistical mechanical analyses of static granular systems and related derivations of expectation values. Second, we establish the existence of an intriguing equipartition principle-the total volume is shared equally amongst both structural and stress-related degrees of freedom. Third, we derive an expression for the compactivity that makes it possible to quantify it from macroscopic measurements.
Earth Science and Engineering and Institute of Shock Physics, Imperial College, London SW7 2BP, United Kingdom.
Raphael
R
Blumenfeld
Joe F
JF
Jordan
Sam F
SF
Edwards
D008956:Models, Chemical; D010316:Particle Size; D013816:Thermodynamics