Granular contact force density of states and entropy in a modified Edwards ensemble.

A method has been found to analyze Edwards' granular contact force probability functional for a special case. As a result, the granular contact force probability density functions are obtained from first principles for this case. The results are in excellent agreement with the experimental and simulation data. The derivation assumes Edwards' flat measure--a density of states (DOS) that is uniform within the metastable regions of phase space. The enabling assumption, supported by physical arguments and empirical evidence, is that correlating information is not significantly recursive through loops in the packing. Maximizing a state-counting entropy results in a transport equation that can be solved numerically. For the present this has been done using the "mean-structure approximation," projecting the DOS across all angular coordinates to more clearly identify its predominant nonuniformities. These features are (1) the grain factor Psi related to grain stability and strong correlation between the contact forces on the same grain and (2) the structure factor Upsilon related to Newton's third law and strong correlation between neighboring grains.