Non-equilibrium Relations for Spin Glasses with Gauge Symmetry

TL;DR

This paper explores how non-equilibrium relations like the Jarzynski equality can be applied to spin glasses with gauge symmetry, providing new analytical insights and methods to evaluate equilibrium properties efficiently.

Contribution

It derives explicit formulas for free-energy differences in spin glasses under gauge symmetry and proposes a method to estimate equilibrium quantities from non-equilibrium data.

Findings

Exponentiated free-energy difference simplifies under gauge symmetry.

Derived a lower bound on work during temperature changes.

Proposed a method to evaluate equilibrium properties from non-equilibrium computations.

Abstract

We study the applications of non-equilibrium relations such as the Jarzynski equality and fluctuation theorem to spin glasses with gauge symmetry. It is shown that the exponentiated free-energy difference appearing in the Jarzynski equality reduces to a simple analytic function written explicitly in terms of the initial and final temperatures if the temperature satisfies a certain condition related to gauge symmetry. This result is used to derive a lower bound on the work done during the non-equilibrium process of temperature change. We also prove identities relating equilibrium and non-equilibrium quantities. These identities suggest a method to evaluate equilibrium quantities from non-equilibrium computations, which may be useful to avoid the problem of slow relaxation in spin glasses.