Fluctuation-dissipation relations in trap models

TL;DR

This paper demonstrates that a specific fluctuation-dissipation relation holds broadly in mean-field trap models, regardless of trap depth distribution, and explores its applicability to models with Glauber dynamics and exponential trap depths.

Contribution

It generalizes a known fluctuation-dissipation relation to a wider class of trap models and examines its validity in different dynamical regimes.

Findings

The relation is valid for all uncorrelated observables in mean-field trap models.

A similar relation holds for Glauber dynamics with exponential trap depths at low temperatures.

The results reveal parallels between energetic and entropic barrier trap models.

Abstract

Trap models are intuitively appealing and often solvable models of glassy dynamics. In particular, they have been used to study aging and the resulting out-of-equilibrium fluctuation-dissipation relations between correlations and response functions. In this note I show briefly that one such relation, first given by Bouchaud and Dean, is valid for a general class of mean-field trap models: it relies only on the way a perturbation affects the transition rates, but is independent of the distribution of trap depths and the form of the unperturbed transition rates, and holds for all observables that are uncorrelated with the energy. The model with Glauber dynamics and an exponential distribution of trap depths, as considered by Barrat and Mezard, does not fall into this class if the perturbation is introduced in the standard way by shifting all trap energies. I show that a similar relation between response and correlation nevertheless holds for the out-of-equilibrium dynamics at low temperatures. The results point to intriguing parallels between trap models with energetic and entropic barriers.