Direct Measurement of Force Configuration Entropy in Jamming

Thermodynamics connects the microscopic details of a system’s entropy to bulk measurements of the system’s properties. In granular systems, for which the thermal energy scale is so small as to be irrelevant, this has been proposed using temperature analogues such as compactivity and angoricity. We present a method of linking the measurements of such quantities to the entropy of the force network by measuring the multiplicity directly. For systems at the critical jamming point there is only one mechanically equilibrium force network compatible with the spring network representation of the system, so the force configurational entropy of a jammed system is zero. For each new contact formed, the dimensionality of the space of allowed force configurations increases by one. Within this space lies a subspace of positive-definite forces, which is compatible with a granular packing. We propose that the volume of this subspace is proportional to the multiplicity of the packing’s force network configuration. To determine the constant of proportionality, we measure the angoricity over 6 decades of pressure using the method of overlapping histograms.