Dynamic Entropy as a Measure of Caging and Persistent Particle Motion in Supercooled Liquids

TL;DR

This paper introduces a dynamic entropy measure based on mean first-passage times to analyze particle motion in supercooled liquids, revealing caging effects and persistent motion, and showing entropy vanishes near the mode-coupling temperature.

Contribution

It presents a novel entropy measure using mean first-passage times to characterize dynamic heterogeneity in supercooled liquids.

Findings

Identifies a cage size where particles are transiently localized.

Detects persistent particle motion beyond the cage scale.

Entropy approaches zero as temperature nears T_c.

Abstract

The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature $T_c$. A number of methods exist for estimating the entropy of dynamical systems and we utilize an approximation based on calculating the mean first-passage time (MFPT) for particle displacement because of its tractability and its accessibility in real and simulation measurements. The MFPT dynamic entropy $S(\epsilon)$ is defined to equal the inverse of the average first-passage time for a particle to exit a sphere of radius $\epsilon$. This measure of the degree of chaotic motion allows us to identify characteristic time and space scales and to quantify the increasingly correlated particle motion and intermittency occurring in supercooled liquids. In particular, we identify a ``cage'' size defining the scale at which the particles are transiently localized, and we observe persistent particle motion at intermediate length scales beyond the scale where caging occurs. Furthermore, we find that the dynamic entropy at the scale of one interparticle spacing extrapolates to zero as the mode-coupling temperature $T_c$ is approached.