A Simple Model for Nonexponential Relaxation in Complex Dynamics

TL;DR

This paper presents a simple diffusion-based model in phase space to explain nonexponential relaxation in complex systems, highlighting how an effective temperature field causes a hierarchy of relaxation times and slow dynamics.

Contribution

It introduces a novel simple model linking diffusion in phase space to nonexponential relaxation, emphasizing the role of an effective temperature field in complex dynamics.

Findings

Hierarchy of relaxation times explains slow relaxation.

Effective temperature field causes nonexponential relaxation.

Model captures complex dynamics in various systems.

Abstract

The nonexponential relaxation ocurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in any time scale becomes apparent in an effective temperature field which leads to a hierarchy of relaxation times responsible for the slow relaxation phenomena.