A procedure to join the force and volume ensemble statistical descriptions of granular media

Granular media consist of a large number discrete particles interacting mostly through contact forces that, being dissipative, jeopardizes classical statistical equilibrium approach based on energy. Instead, two independent descriptions have been proposed: the Volume Ensemble and Force Network Ensemble. Hereby, we propose procedure to join them into single description, using Discrete Element simulations granular medium monodisperse spheres in limit state isotropic compression as testing ground. By classifying grains according faces Voronoï cells around them, our analysis establishes an empirical relationship between that contacts grain. In addition, linear each cell elementary proposed by T. Aste Di Matteo 2007 is found. From those relations, expression for total entropy (volumes plus forces) written terms number, when maximized, gives equation connecting angoricity (the temperature-like variable force network ensemble) compactivity volume ensemble). So, microscopic connection geometry mechanics and, constitutes further step towards building complete theory equilibrium.