A Tiling Approach to Counting Inherent Structures in Hard Potential Systems

TL;DR

This paper introduces a tiling-based method to count inherent structures in hard potential systems, providing a geometric framework that simplifies understanding of jammed configurations in glass-forming liquids.

Contribution

It develops a novel tiling approach that constructs and counts collectively jammed packings using geometric incompatibility rules, advancing the theoretical understanding of inherent structures.

Findings

The approach effectively counts inherent structures in hard disc systems.

Geometric quantities like tile compatibility relate to the number of inherent structures.

Simplifications occur in highly confined hard disc systems.

Abstract

The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure corresponds to a collectively jammed configuration. This work develops a tiling based approach to counting inherent structures that constructs packings by combining sets of elementary locally jammed structures but eliminates those final packings that either, do not tile space, or are not collectively jammed, through the use of tile incompatibility rules. The resulting theory contains a number of geometric quantities, such as the number of growth sites on a tile and the number of tile compatibilities that provide insight into the number of inherent structures in certain limits. We also show that these geometric quantities become quite simple in a system of highly confined hard discs.