Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming

TL;DR

This study uses simulations to test Edwards' conjecture, providing evidence that at the unjamming point, all packings of soft particles are equally probable, supporting the idea of a uniform distribution of jammed states.

Contribution

The paper offers the first direct simulation-based evidence that all packings are equally likely at the unjamming point, validating Edwards' hypothesis.

Findings

All packings are equally probable at unjamming.

Configurational entropy is maximal at unjamming.

Supports Edwards' statistical-mechanical framework.

Abstract

In the late 1980s, Sam Edwards proposed a possible statistical-mechanical framework to describe the properties of disordered granular materials. A key assumption underlying the theory was that all jammed packings are equally likely. In the intervening years it has never been possible to test this bold hypothesis directly. Here we present simulations that provide direct evidence that at the unjamming point, all packings of soft repulsive particles are equally likely, even though generically, jammed packings are not. Typically, jammed granular systems are observed precisely at the unjamming point since grains are not very compressible. Our results therefore support Edwards' original conjecture. We also present evidence that at unjamming the configurational entropy of the system is maximal.