Power-law decay in first-order relaxation processes

TL;DR

This paper demonstrates that first-order relaxation processes tend to follow a power-law decay near the stationary state and introduces a graphical method to distinguish between power-law and stretched exponential decays, supported by experimental and simulated data.

Contribution

It provides a new graphical approach to differentiate decay types in relaxation processes and confirms the prevalence of power-law decay near stationarity.

Findings

Power-law decay fits experimental relaxation data near stationarity.

Graphical method effectively discriminates between power-law and stretched exponential decays.

Supported by magnetic, dielectric, and simulated data.

Abstract

Starting from a simple definition of stationary regime in first-order relaxation processes, we obtain that experimental results are to be fitted to a power-law when approaching the stationary limit. On the basis of this result we propose a graphical representation that allows the discrimination between power-law and stretched exponential time decays. Examples of fittings of magnetic, dielectric and simulated relaxation data support the results.