Nonequilibrium relations in spin glasses

TL;DR

This paper explores nonequilibrium relations like the Jarzynski equality in spin glasses, revealing a new link between nonequilibrium processes and equilibrium averages, which could improve optimization methods.

Contribution

It introduces a novel relationship connecting nonequilibrium processes with equilibrium averages in spin glasses, aiding in overcoming critical slowing down.

Findings

Discovered a new relation between nonequilibrium averages and equilibrium thermal averages.

Proposed a potential method to mitigate critical slowing down in spin glasses.

Suggested applications to hard combinatorial optimization problems.

Abstract

The applications of nonequilbrium relations such as the Jarzynski equality and the fluctuation theorem to spin glasses are considered. The spin glass is a basic platform where we consider an application of an approximate solver of combinatorial optimization problems, simulated annealing. We find a novel relationship between an average through a nonequilibrium process where the temperature changes as in simulated annealing and a thermal average in equilibrium with different amounts of quenched randomness. The results shown in the present study may serve as an alternative way to overcome critical slowing down in spin glasses. It means that this way may mitigate difficulties in several hard optimization problems.