Relaxation patterns and semi-Markov dynamics

TL;DR

This paper explores complex relaxation patterns in physical systems, using semi-Markov processes and Bernstein functions to unify various approaches and better understand non-exponential relaxation behaviors.

Contribution

It introduces a unified framework based on Bernstein functions to analyze diverse relaxation patterns via semi-Markov processes, extending beyond traditional exponential models.

Findings

Unified approach to relaxation patterns using Bernstein functions

Characterization of semi-Markov processes for non-exponential relaxation

Connections between fractional derivatives and relaxation behaviors

Abstract

Exponential relaxation to equilibrium is a typical property of physical systems, but inhomogeneities are known to distort the exponential relaxation curve, leading to a wide variety of relaxation patterns. Power law relaxation is related to fractional derivatives in the time variable. More general relaxation patterns are considered here, and the corresponding semi-Markov processes are studied. Our method, based on Bernstein functions, unifies three different approaches in the literature.