Direct determination of the size of basins of attraction of jammed solids

TL;DR

This paper introduces a Monte Carlo method based on free energy to measure the size of basins of attraction in jammed solids, enabling estimation of the number of distinct minima even in large systems.

Contribution

The paper presents a novel free-energy Monte Carlo approach to quantify basin volumes and estimate the number of jammed states in large particle packings.

Findings

Entropy of jammed packings is extensive.

Number of jammed states can be estimated even when too large to sample directly.

Entropy of packings has a maximum at a certain packing fraction.

Abstract

We propose a free-energy based Monte-Carlo method to measure the volume of potential-energy basins in configuration space. Using this approach we can estimate the number of distinct potential-energy minima, even when this number is much too large to be sampled directly. We validate our approach by comparing our results with the direct enumeration of distinct jammed states in small packings of frictionless spheres. We find that the entropy of distinct packings is extensive and that the entropy of distinct hard-sphere packings must have a maximum as a function of packing fraction.