Entropy of jammed matter

TL;DR

This paper explores the entropy of jammed matter, revealing how disorder varies between different packing states and providing equations relating entropy, volume, and compactivity.

Contribution

It introduces a novel approach to calculating the entropy of jammed packings using force and volume ensembles, and clarifies the disorder in loose versus close packings.

Findings

Entropy vanishes at random close packing

Loose packings are more disordered than close packings

Equations of state relate entropy, volume fraction, and compactivity

Abstract

We investigate the nature of randomness in disordered packings of frictional spheres. We calculate the entropy of 3D packings through the force and volume ensemble of jammed matter, a mesoscopic ensemble and numerical simulations using volume fluctuation analysis and graph theoretical methods. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter. At the mesoscopic level the entropy vanishes at random close packing. The entropy of the jammed system reveals that the random loose packings are more disordered than random close packings, allowing for an unambiguous interpretation of both limits.