Devising a protocol-related statistical mechanics framework for granular materials

TL;DR

This paper develops a statistical mechanics framework for jammed granular materials, linking protocol-dependent entropy to ensemble equivalences and challenging existing assumptions about Edwards' ensemble.

Contribution

It introduces a protocol-related microcanonical ensemble for granular materials, extending previous work and clarifying the nature of statistical ensembles in these systems.

Findings

Protocol can be viewed as a canonical ensemble with a specific temperature

Large system sizes show Gaussianity, indicating ensemble equivalence

The proposed microcanonical ensemble differs from Edwards' original ensemble

Abstract

Devising a statistical mechanics framework for jammed granular materials is a challenging task as those systems do not share some important properties required to characterize them with statistical thermodynamics tools. In a recent paper [Asenjo et al. PRL, 2014], a new definition of a granular entropy, that puts the protocol used to generate the packings at its roots, has been proposed. Following up these results, it is shown that the protocol used in [Asenjo et al. PRL, 2014] can be recast as a canonical ensemble with a particular value of the temperature. Signature of gaussianity for large system sizes strongly suggests an asymptotic equivalence with a corresponding microcanonical ensemble where jammed states with certain basin volumes are sampled uniformly. We argue that this microcanonical ensemble is not Edwards' microcanonical ensemble and generalize this argument to other protocols.