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.