Entropy of particle packings : an illustration on a toy model

TL;DR

This paper introduces a toy model for particle packings using hexagons on a triangular lattice, analytically calculating the exponential growth of stable packings to illustrate packing entropy.

Contribution

It provides an analytical computation of stable packing counts in a simplified model, highlighting entropy in disordered particle arrangements.

Findings

Number of stable packings grows exponentially with lattice size

Entropy concept illustrated through analytical results

Disordered bidispersed case analyzed in detail

Abstract

A toy model of particles packings is presented, which consists in arranging hexagons on a triangular lattice according to local stability rules. The number of stable packings is analytically computed and found to grow exponentially with the size of the lattice, which illustrates the concept of packing entropy first proposed by Edwards and collaborators. The analysis is carried out for both the monodispersed case and the more interesting, i.e. more disordered, bidispersed case.