Geometric partition functions of cellular systems: Explicit calculation of the entropy in two and three dimensions

TL;DR

This paper introduces a method to calculate the entropy of cellular structures in 2D and 3D using Hamiltonian-like volume functions, accounting for geometrical correlations systematically.

Contribution

It develops a formalism for explicit entropy calculation in cellular systems, extending the compactivity concept to both two and three dimensions.

Findings

Explicit formulas for mean vertex density as a function of compactivity.

Porosity fluctuations are characterized in terms of compactivity.

The method applies equally to 2D and 3D granular assemblies.

Abstract

A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling the identification of a phase space and making it possible to take account of geometrical correlations systematically. Case studies are presented for which explicit calculations of the mean vertex density and porosity fluctuations are given as functions of compactivity. The formalism applies equally well to two- and three-dimensional granular assemblies.