Positional information as a universal predictor of freezing

TL;DR

This study uncovers a universal relation between positional information, quantified by two-body excess entropy, and the freezing transition in a 2D system, revealing a scaling law that links entropy to temperature near freezing.

Contribution

The paper introduces a universal scaling law connecting two-body excess entropy with freezing temperature in a 2D system, advancing understanding of phase transition indicators.

Findings

A master relation between two-body excess entropy and freezing temperature.

A derived scaling law: $- ext{S}_2 \\sim |T_f - T|^{-1/3}$.

Discussion of universality in positional information at phase transitions.

Abstract

Variation of positional information, measured by the two-body excess entropy $\mathsf{S}_\mathrm{2}$, is studied across the liquid-solid equilibrium transition in a simple two-dimensional system. Analysis reveals a master relation between $\mathsf{S}_\mathrm{2}$ and the freezing temperature $T_{\mathrm{f}}$, from which a scaling law is extracted: $-\mathsf{S}_\mathrm{2}\sim |T_{\mathrm{f}} - T| ^{-1/3}$. Theoretical and practical implications of the observed universality are discussed.