Generalized fluctuation-dissipation theorem in a soluble out of equilibrium model

TL;DR

This paper extends the fluctuation-dissipation theorem to an exactly solvable out-of-equilibrium model, introducing a modified relation with an effective temperature that varies with time scales.

Contribution

It provides a generalized fluctuation-dissipation relation applicable to out-of-equilibrium systems with a time-dependent effective temperature.

Findings

Derived a modified fluctuation-dissipation relation for the model

Showed the effective temperature depends explicitly on time scales

Validated the relation within the solvable model

Abstract

In the context of an exactly soluble out of equilibrium (quenched) model, we study an extension of the fluctuation-dissipation relation. This involves a modified differential form of this relation, with an effective temperature which may have an explicit dependence on time scales.