Granular entropy: Explicit calculations for planar assemblies

TL;DR

This paper introduces a new volume function based on a geometric tensor to calculate the entropy of planar granular assemblies, enabling explicit mean volume and fluctuation calculations with a rigorously additive property.

Contribution

It presents a novel volume function derived from a geometric tensor that simplifies entropy calculations for planar granular systems.

Findings

Explicit formulas for mean volume and fluctuations

The volume function is rigorously additive

Application to case studies demonstrates utility

Abstract

This paper proposes a new volume function for calculation of the entropy of planar granular assemblies. This function is extracted from the antisymmetric part of a new geometric tensor and is rigorously additive when summed over grains. It leads to the identification of a conveniently small phase space. The utility of the volume function is demonstrated on several case studies, for which we calculate explicitly the mean volume and the volume fluctuations.