Relaxation at late stages in an entropy barrier model for glassy systems

TL;DR

This paper analyzes the relaxation dynamics of a recently proposed entropy barrier model for glassy systems, deriving analytical expressions for relaxation times and bounds based on system size.

Contribution

It introduces a simplified Ehrenfest urn model variant to describe late-stage relaxation in glassy systems and provides analytical bounds for relaxation times.

Findings

Derived explicit relaxation time expressions.

Established bounds for relaxation times as a function of system size.

Connected the model's dynamics to a simple urn model.

Abstract

The ground state dynamics of an entropy barrier model proposed recently for describing relaxation of glassy systems is considered. At stages of evolution the dynamics can be described by a simple variant of the Ehrenfest urn model. Analytical expression for the relaxation times from an arbitrary state to the ground state is derived. Upper and lower bounds for the relaxation times as a function of system size are obtained.