Continuous-time random walk model of relaxation of two-state systems

TL;DR

This paper models the relaxation behavior of two-state systems using a continuous-time random walk approach, revealing how different waiting time distributions influence relaxation dynamics, including non-monotonic and slow relaxation phenomena.

Contribution

It introduces a CTRW-based framework to analyze two-state system relaxation, highlighting effects of Erlang and heavy-tailed waiting time distributions on relaxation regimes.

Findings

Non-monotonic relaxation possible under certain conditions

Heavy tails lead to slow relaxation

Superheavy tails cause superslow relaxation

Abstract

Using the continuous-time random walk (CTRW) approach, we study the phenomenon of relaxation of two-state systems whose elements evolve according to a dichotomous process. Two characteristics of relaxation, the probability density function of the waiting times difference and the relaxation law, are of our particular interest. For systems characterized by Erlang distributions of waiting times, we consider different regimes of relaxation and show that, under certain conditions, the relaxation process can be non-monotonic. By studying the asymptotic behavior of the relaxation process, we demonstrate that heavy and superheavy tails of waiting time distributions correspond to slow and superslow relaxation, respectively.