Origin of the Violation of the Fluctuation-Dissipation Theorem in Systems with Activated Dynamics

TL;DR

This paper investigates why the fluctuation-dissipation theorem fails in systems with slow, activated dynamics, revealing that the violation is due to eliminating fast variables and questioning the robustness of the effective temperature concept.

Contribution

It provides a theoretical analysis linking the violation to activated dynamics and challenges the universality of effective temperature in glassy systems.

Findings

Violation arises from elimination of fast variables

Effective temperature is observable-dependent and can diverge or be negative

Violation is intrinsically related to activated nature of slow relaxation

Abstract

We analyze the validity of the fluctuation-dissipation theorem for slow relaxation systems in the context of mesoscopic nonequilibrium thermodynamics. We demonstrate that the violation arises as a natural consequence of the elimination of fast variables in the description of a glassy system, and it is intrinsically related to the underlying activated nature of slow relaxation. In addition, we show that the concept of effective temperature, introduced to characterize the magnitude of the violation, is not robust since it is observable-dependent, can diverge, or even be negative.