On a non-linear Fluctuation Theorem for the aging dynamics of disordered trap models

TL;DR

This paper derives a non-linear Fluctuation Theorem for the aging dynamics of disordered trap models, revealing regimes of linear response and simple relations in non-linear response, driven by a dynamical symmetry.

Contribution

It introduces a novel non-linear Fluctuation Theorem specific to disordered trap models, highlighting unique aging and response behaviors not seen in other disordered systems.

Findings

Existence of a linear response regime with Fluctuation-Dissipation relation validity during aging.

Characteristic time limit for linear response depending on external force.

Simple relation for asymmetry in diffusion fronts in non-linear response regime.

Abstract

We consider the dynamics of the disordered trap model, which is known to be completely out-of-equilibrium and to present strong localization effects in its aging phase. We are interested into the influence of an external force, when it is applied from the very beginning at $t=0$, or only after a waiting time $t_w$. We obtain a "non-linear Fluctuation Theorem" for the corresponding one-time and two-time diffusion fronts in any given sample, that implies the following consequences : (i) for fixed times, there exists a linear response regime, where the Fluctuation-Dissipation Relation or Einstein relation is valid even in the aging time sector, in contrast with other aging disordered systems; (ii) for a fixed waiting time and fixed external field, the validity of the linear response regime is limited in time by a characteristic time depending on the external force; (iii) in the non-linear response regime, there exists a very simple relation for the asymmetry in the position for the one-time and the two-times disorder averaged diffusion fronts in the presence of an external force, in contrast to other models of random walks in random media. The present non-linear Fluctuation Theorem is a consequence of a special dynamical symmetry of the trap model.