A Model for Nonexponential Relaxation and Aging in Dissipative Systems

TL;DR

This paper presents a model explaining nonexponential relaxation and aging in dissipative systems via diffusion in phase space influenced by nonconservative forces, introducing an effective temperature and a hierarchy of relaxation times.

Contribution

It introduces a novel model linking nonconservative forces to aging phenomena and nonexponential relaxation in dissipative systems, incorporating a generalized fluctuation-dissipation relation.

Findings

Hierarchy of relaxation times explains aging.

Effective temperature characterizes nonequilibrium states.

Relation similar to Vogel-Fulcher-Tammann law observed.

Abstract

The nonexponential relaxation and aging inherent to complex dynamics manifested in a wide variety of dissipative systems is analyzed through a model of diffusion in phase space in the presence of a nonconservative force. The action of this force establishes a heat flow which maintains the system away from equilibrium. The inability of the system to find its equilibrium state becomes apparent through the presence of an effective temperature field. This is the temperature of the stationary nonequilibrium state reached by the system satisfying a generalyzed version of the fluctuation-dissipation theorem. The presence of a nonequilibrium temperature leads to a hierarchy of relaxation times responsible for the aging phenomena and to a relation similar to the Vogel-Fulcher-Tammann law.