Angoricity and compactivity describe the jamming transition in soft particulate matter

TL;DR

This paper explores how concepts from equilibrium statistical mechanics, specifically angoricity and compactivity, can describe the jamming transition in soft particulate matter by comparing dynamic configurations with ensemble averages.

Contribution

It demonstrates the applicability of the volume-stress ensemble to out-of-equilibrium jammed systems and clarifies the thermodynamic nature of the jamming transition.

Findings

Agreement between dynamic and ensemble configurations suggests ergodicity.

Absence of critical fluctuations indicates a non-critical jamming transition.

Calculations of entropy, pressure, and force distributions reveal scaling laws near jamming.

Abstract

The application of concepts from equilibrium statistical mechanics to out-of-equilibrium systems has a long history of describing diverse systems ranging from glasses to granular materials. For dissipative jammed systems-- particulate grains or droplets-- a key concept is to replace the energy ensemble describing conservative systems by the volume-stress ensemble. Here, we test the applicability of the volume-stress ensemble to describe the jamming transition by comparing the jammed configurations obtained by dynamics with those averaged over the ensemble as a probe of ergodicity. Agreement between both methods suggests the idea of "thermalization" at a given angoricity and compactivity. We elucidate the thermodynamic order of the jamming transition by showing the absence of critical fluctuations in static observables like pressure and volume. The approach allows to calculate observables such as the entropy, volume, pressure, coordination number and distribution of forces to characterize the scaling laws near the jamming transition from a statistical mechanics viewpoint.