Is there a Granular Potential?

TL;DR

This paper introduces a granular potential within the Edwards ensemble to better understand equilibrium and mass transport in granular systems, supported by simulations and analytical models that reveal how entropy and potential differences drive system behavior.

Contribution

It proposes a new granular potential concept analogous to chemical potential, expanding the statistical mechanics framework for granular materials.

Findings

Granular potential influences equilibrium between systems exchanging volume and particles.

Mass moves from high to low ratios of granular potential to compactivity.

Adding particles increases entropy at high compactivity but decreases it at low compactivity.

Abstract

Granular materials, such as sand or grain, exhibit many structural and dynamic characteristics similar to those observed in molecular systems, despite temperature playing no role in their properties. This has led to an effort to develop a statistical mechanics for granular materials that has focused on establishing an equivalent to the microcanonical ensemble and a temperature-like thermodynamic variable. Here, we expand on these ideas by introducing a granular potential into the Edwards ensemble, as an analogue to the chemical potential, and explore its properties using a simple model of a granular system. A simple kinetic Monte Carlo simulation of the model shows the effect of mass transport leading to equilibrium and how this is connected to the redistribution of volume in the system. An exact analytical treatment of the model shows that the compactivity and the ratio of the granular potential to the compactivity determine the equilibrium between two open systems that are able to exchange volume and particles, and that mass moves from high to low values of this ratio. Analysis of the granular potential shows that adding a particle to the system increases the entropy at high compactivity, but decreases the entropy at low compactivity. Finally, we demonstrate the use of a small system thermodynamics method for the measurement of granular potential differences.