Stimulated and spontaneous relaxation in glassy systems

TL;DR

This paper investigates two relaxation processes in glassy systems, demonstrating that different effective temperatures derived from various methods coincide in a simplified aging scenario, supporting a statistical view of non-equilibrium temperature.

Contribution

It introduces a simplified partial equilibration scenario in aging systems and shows the equivalence of multiple effective temperature definitions, reinforcing their physical significance.

Findings

All three effective temperatures coincide in the partial equilibration scenario.

The study confirms the statistical nature of non-equilibrium temperature in aging systems.

Results are validated in a simple model system.

Abstract

Recent numerical simulations of a disordered system (Preprint arXiv:condmat/0307554) have shown the existence of two different relaxational processes (called stimulated and spontaneous) characterizing the relaxation observed in structural glasses. The existence of these two processes has been claimed to be at the roots of the intermittency phenomenon observed in recent experiments. Here we consider a generic system put in contact with a bath at temperature T and characterized by an adiabatic slow relaxation (i.e. by a negligible net heat flow from the system to the bath) in the aging state. We focus on a simplified scenario (termed as partial equilibration) characterized by the fact that $=0 (where only the spontaneous process is observable) and whose microscopic stochastic dynamics is ergodic when constrained to the constant energy surface. Three different effective temperatures can be defined: a) from the fluctuation-dissipation theorem (FDT), b) from a fluctuation theorem describing the statistical distribution of heat exchange events between system and bath and c) from a set of observable-dependent microcanonical relations in the aging state. In a partial equilibration scenario we show how all three temperatures coincide reinforcing the idea that a statistical (rather than thermometric) definition of a non-equilibrium temperature is physically meaningful in aging systems. These results are explicitly checked in a simple model system