Equivalence of driven and ageing fluctuation-dissipation relations in the trap model

TL;DR

This paper demonstrates that in a trap model, the fluctuation-dissipation relations for neutral observables are essentially equivalent in driven steady states and aged systems, highlighting a universal aspect of non-equilibrium glassy dynamics.

Contribution

It extends previous work on ageing fluctuation-dissipation relations by showing their equivalence in driven steady states for neutral observables in a trap model.

Findings

FD relations are similar in driven and aged states for neutral observables

The equivalence holds with small corrections in driven systems

Robustness of the relation is analyzed against observable non-neutrality and different driving mechanisms

Abstract

We study the non-equilibrium version of the fluctuation dissipation (FD) relation in the glass phase of a trap model that is driven into a non-equilibrium steady state by external ``shear''. This extends our recent study of ageing FD relations in the same model, where we found limiting, observable independent FD relations for ``neutral'' observables that are uncorrelated with the system's average energy. In this work, for such neutral observables, we find the FD relation for a stationary weakly driven system to be the same, to within small corrections, as for an infinitely aged system. We analyse the robustness of this correspondence with respect to non-neutrality of the observable, and with respect to changes in the driving mechanism.