Microscopic explanation of non-Debye relaxation for heat transfer

TL;DR

This paper provides a microscopic explanation for both Debye and non-Debye heat transfer relaxation processes, linking them to first passage phenomena and survival probabilities, especially under broken ergodicity conditions.

Contribution

It introduces a microscopic framework connecting relaxation functions to survival probabilities and explains non-Debye relaxation via broken ergodicity and first passage analysis.

Findings

Survival probability decays as a power law S(t)=τ/t in broken ergodicity cases

Relates relaxation functions to first passage phenomena

Provides microscopic insight into non-Debye relaxation mechanisms

Abstract

We give a microscopic explanation of both Debye and non-Debye thermalization processes that have been recently reported by Gall and Kutner (Physica A 352, 347 (2005)). Due to reduction of the problem to first passage phenomena we argue that relaxation functions f(t) introduced by the authors directly correspond to survival probabilities S(t) of particles in the considered systems. We show that in the case of broken ergodicity (i.e. in the case of mirror collisions) the survival probability decays as a power law S(t)=\tau/t.