Force balance in canonical ensembles of static granular packings

TL;DR

This paper explores how local force balance influences the transition from microcanonical to canonical ensembles in static granular packings, using analytical relations and first canonical simulations of the force network ensemble.

Contribution

It introduces analytical relations linking stress, tiling area, and their fluctuations, and demonstrates ensemble equivalence through canonical simulations of the force network ensemble.

Findings

Force balance leads to invariant tiling area in microcanonical ensembles.

Canonical ensembles can be characterized by an intensive thermodynamic parameter.

First canonical simulations of the force network ensemble confirm ensemble equivalence.

Abstract

We investigate the role of local force balance in the transition from a microcanonical ensemble of static granular packings, characterized by an invariant stress, to a canonical ensemble. Packings in two dimensions admit a reciprocal tiling, and a collective effect of force balance is that the area of this tiling is also invariant in a microcanonical ensemble. We present analytical relations between stress, tiling area and tiling area fluctuations, and show that a canonical ensemble can be characterized by an intensive thermodynamic parameter conjugate to one or the other. We test the equivalence of different ensembles through the first canonical simulations of the force network ensemble, a model system.