Avalanche dynamics and nonexponential relaxation

TL;DR

This paper proposes that self-organized criticality (SOC) and avalanche dynamics explain the common nonexponential relaxation in complex systems, linking it to stretched exponential decay and 1/f noise, with a mean-field approach predicting exponential relaxation.

Contribution

It introduces a theoretical framework connecting SOC, avalanche dynamics, and relaxation phenomena, deriving specific scaling laws and spectral properties.

Findings

Normalized relaxation follows a stretched exponential decay.

Frequency spectrum exhibits 1/f noise.

Mean-field approach predicts exponential relaxation.

Abstract

The theory of SOC, and related avalanche dynamics, is proposed as the origin of the ubiquitous nonexponential relaxation observed in complex systems. Introducing some scaling laws and relations we have obtained that the normalized relaxation function follows an stretched exponential decay and that the frequency spectrum follows a "1/f" noise. Moreover, in the MF aproach the relaxation is found to be exponential.