Entropy Maximization in the Force Network Ensemble for Granular Solids

A long-standing issue in the area of granular media is the tail of the force distribution, in particular, whether this is exponential, Gaussian, or even some other form. Here we resolve the issue for the case of the force network ensemble in two dimensions. We demonstrate that conservation of the total area of a reciprocal tiling, a direct consequence of local force balance, is crucial for predicting the local stress distribution. Maximizing entropy while conserving the tiling area and total pressure leads to a distribution of local pressures with a generically Gaussian tail that is in excellent agreement with numerics, both with and without friction and for two different contact networks.