Entropic Origin of the Growth of Relaxation Times in Simple Glassy Liquids

TL;DR

This paper investigates the increase in relaxation times in simple glassy liquids, attributing it mainly to entropic effects that make finding connecting saddle points between minima more difficult as density increases.

Contribution

It introduces a numerical study linking the growth of free energy barriers to entropic effects, supporting the Vogel-Fulcher law in dense hard-sphere systems.

Findings

Free energy barriers grow with density following Vogel-Fulcher law

Transition probabilities decrease due to entropic effects

Growth in relaxation times is primarily entropic in origin

Abstract

Transitions between ``glassy'' local minima of a model free-energy functional for a dense hard-sphere system are studied numerically using a ``microcanonical'' Monte Carlo method that enables us to obtain the transition probability as a function of the free energy and the Monte Carlo ``time''. The growth of the height of the effective free energy barrier with density is found to be consistent with a Vogel-Fulcher law. The dependence of the transition probability on time indicates that this growth is primarily due to entropic effects arising from the difficulty of finding low-free-energy saddle points connecting glassy minima.