Derivation of the spin-glass order parameter from stochastic thermodynamics

TL;DR

This paper introduces a fluctuation relation to determine the spin-glass order parameter function in weakly ergodic systems by analyzing entropy production fluctuations, validated across glassy models and potentially applicable to other nonequilibrium systems.

Contribution

It presents a novel fluctuation relation method to extract the order parameter function $q(x)$ in aging systems, linking entropy fluctuations to the system's overlap structure.

Findings

Entropy production fluctuations are Gaussian at fixed overlap $q$.

The derived quasi-FDT characterizes aging systems.

Validation across various glassy models confirms the method's effectiveness.

Abstract

A fluctuation relation is derived to extract the order parameter function $q(x)$ in weakly ergodic systems. The relation is based on measuring and classifying entropy production fluctuations according to the value of the overlap $q$ between configurations. For a fixed value of $q$, entropy production fluctuations are Gaussian distributed allowing us to derive the quasi-FDT so characteristic of aging systems. The theory is validated by extracting the $q(x)$ in various types of glassy models. It might be generally applicable to other nonequilibrium systems and experimental small systems.