# Mapping Disorder in Entropically Ordered Crystals

## TL;DR

This paper investigates how entropy is distributed in crystals of hard hexagons, revealing that translational degrees of freedom dominate entropy near key phase transitions, through a mode decomposition approach.

## Contribution

It introduces a method to decompose thermal fluctuations into collective modes, extending Onsager's theory to quantify entropy contributions in hard shape crystals.

## Key findings

- Translational entropy dominates near densest packing.
- Rotational entropy is less significant in the studied regimes.
- The approach generalizes Onsager's theory to complex crystal systems.

## Abstract

Systems of hard shapes crystallize due to entropy. How is entropy distributed among translational and rotational microscopic contributions? We answer this question by decomposing thermal fluctuation of crystals of hard hexagons into collective modes, a generalization and quantification of the Onsager picture of hard rod liquid crystals. We show that at densities both near densest packing and near the solid-hexatic melting transition, solids of hard regular hexagons hold most of their entropy in translational degrees of freedom.