A Free Energy Landscape for Cage Breaking of Three Hard Disks

TL;DR

This study models the cage-breaking process of three hard disks in a confined space, revealing how the free energy landscape governs transition times and highlighting the limitations of one-dimensional representations in complex systems.

Contribution

It introduces an exact free energy landscape for a three-disk system and analyzes its implications for understanding cage-breaking dynamics in dense particle systems.

Findings

Cage-breaking times follow Arrhenius scaling with energy barrier height.

The free energy landscape can be exactly computed as a function of system size.

One-dimensional models may oversimplify multi-dimensional diffusion behaviors.

Abstract

We investigate cage breaking in dense hard disk systems using a model of three Brownian disks confined within a circular corral. This system has a six-dimensional configuration space, but can be equivalently thought to explore a symmetric one-dimensional free energy landscape containing two energy minima separated by an energy barrier. The exact free energy landscape can be calculated as a function of system size. Results of simulations show the average time between cage breaking events follows an Arrhenius scaling when the energy barrier is large. We also discuss some of the consequences of using a one-dimensional representation to understand dynamics in a multi-dimensional space, such as diffusion acquiring spatial dependence and discontinuities in spatial derivatives of free energy.