The Glass Transition and the Jarzynski Equality

TL;DR

This paper explores the application of the Jarzynski Equality to glass formation, demonstrating how it can be used to compute free energy differences in history-dependent glassy states, and deriving new variants relevant to nonequilibrium conditions.

Contribution

It introduces new variations of the Jarzynski Equality applicable to nonequilibrium glassy states, enabling consistent free energy calculations for history-dependent systems.

Findings

Jarzynski Equality relates to free energy differences in glass formation.

Derived new variants of the Jarzynski Equality for nonequilibrium states.

Provided methods to compute free energy consistent with entropy and second law.

Abstract

A simple model featuring a double well potential is used to represent a liquid that is quenched from an ergodic state into a history dependent glassy state. Issues surrounding the application of the Jarzynski Equality to glass formation are investigated. We demonstrate that the Jarzynski Equality gives the free energy difference between the initial state and the state we would obtain if the glass relaxed to true thermodynamic equilibrium. We derive new variations of the Jarzynski Equality which are relevant to the history dependent glassy state rather than the underlying equilibrium state. It is shown how to compute the free energy differences for the nonequilibrium history dependent glassy state such that it remains consistent with the standard expression for the entropy and with the second law inequality.