Thermal properties of slow dynamics

TL;DR

This paper explores the thermal properties and slow dynamics of relaxing and driven systems, revealing multiple coexisting temperatures and modified fluctuation-dissipation relations, with implications for understanding non-equilibrium states.

Contribution

It introduces a scenario with multiple coexisting temperatures and partial equilibrations, challenging traditional Gibbs-Boltzmann assumptions in non-equilibrium systems.

Findings

Multiple temperatures act on different timescales.

Modified fluctuation-dissipation relations are predicted.

Experimental verification of reciprocity relations is feasible.

Abstract

The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the Gibbs-Boltzmann distribution, or a small departure from it. Interesting cases in which it is not are glasses, phase-separation, and certain driven complex fluids. We describe a scenario with several coexisting temperatures acting on different timescales, and partial equilibrations at each time scale. This scenario entails strong modifications of the fluctuation-dissipation equalities and the existence of some unexpected reciprocity relations. Both predictions are open to experimental verification, particularly the latter. The construction is consistent in general, since it can be viewed as the breaking of a symmetry down to a residual group. It does not assume the presence of quenched disorder. It can be -- and to a certain extent has been -- tested numerically, while some experiments are on their way. There is furthermore the perspective that analytic arguments may be constructed to prove or disprove its generality.