Relation between Entropy, Diffusion and Relaxation Kinetics

TL;DR

This paper explores the relationship between entropy, diffusion, and relaxation kinetics, proposing new bounds and expressions that incorporate many-body correlations and are validated through simulations and theoretical analysis.

Contribution

It introduces an improved relation between diffusion and entropy that accounts for multi-site correlations and applies it to various systems including colloids and energy landscapes.

Findings

Lower bound becomes equality when certain correlations are neglected.

Derived an accurate expression matching computer simulations.

Mode-coupling theory combined with the inequality estimates entropy from correlations.

Abstract

Intermolecular correlations lower values of both diffusion and entropy. We present an analysis of the existing relations between long-time diffusion (D) and entropy. S. A recently proposed inequality, a lower bound, by Sorkin et al., expresses the long-time diffusion in terms of diffusion in a reference state and the entropy difference. Such a relationship may provide a measure of intermolecular correlations. We show that for a one-dimensional rugged energy landscape, the lower bound becomes equality only if certain three-site correlations are neglected. When these correlations are included, we can derive an accurate expression that agrees with computer simulations. The strong dimensionality dependence of diffusion of a Brownian particle in a rugged energy landscape also resembles the recently proposed inequality. We show that for interacting colloids, a mode-coupling theory-type calculation of diffusion coefficient can be combined with the new inequality to estimate entropy change from long-range inter-colloid correlations. Interestingly, the rate of barrier crossing in a multidimensional potential energy surface, related to diffusion in a periodic lattice, is shown to admit a relation that depends on the entropy change in a way reminiscent of the relation between D and S.