An experimental test of volume-equilibration between granular systems

TL;DR

This paper experimentally tests the concept of volume-based temperature analogs in granular systems, revealing that compactivity does not equilibrate between different materials, but a new material-independent relationship emerges.

Contribution

The study demonstrates the failure of compactivity to equilibrate and introduces a new material-independent equation of state based on packing fraction fluctuations.

Findings

Compactivity does not equilibrate between granular subsystems.

A new equation of state relates mean and fluctuations of packing fraction.

An intensive parameter decoupled from volume statistics is identified.

Abstract

Understanding granular and other athermal systems requires the identification of state variables which consistently predict their bulk properties. A promising approach has been to draw on the techniques of equilibrium statistical mechanics, but to consider alternate conserved quantities in place of energy. The Edwards ensemble, based on volume conservation, provides a temperaturelike intensive parameter called compactivity. We present experiments which demonstrate the failure of compactivity to equilibrate (via volume-exchange) between a pair of externally-agitated granular subsystems with different material properties. Nonetheless, we identify a material-independent relationship between the mean and fluctuations of the local packing fraction which forms the basis for an equation of state. This relationship defines an intensive parameter that decouples from the volume statistics.