Derivation of the spin-glass order parameter from stochastic thermodynamics

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.