Linear Response and Fluctuation Dissipation Theorem for non-Poissonian Renewal Processes

TL;DR

This paper develops a theoretical framework using CTRW to analyze non-Poissonian relaxation, deriving two distinct fluctuation-dissipation theorems for different perturbation mechanisms in non-ergodic systems.

Contribution

It introduces a novel analytical approach to non-Poissonian relaxation, deriving two specific fluctuation-dissipation theorems for different perturbation mechanisms.

Findings

Derived fluctuation-dissipation theorems for non-Poissonian CTRW models

Analyzed system response under bias and event-time perturbations

Provided analytical solutions in non-ergodic regimes

Abstract

The Continuous Time Random Walk (CTRW) formalism is used to model the non-Poisson relaxation of a system response to perturbation. Two mechanisms to perturb the system are analyzed: a first in which the perturbation, seen as a potential gradient, simply introduces a bias in the hopping probability of the walker from on site to the other but leaves unchanged the occurrence times of the attempted jumps ("events") and a second in which the occurrence times of the events are perturbed. The system response is calculated analytically in both cases in a non-ergodic condition, i.e. for a diverging first moment in time. Two different Fluctuation-Dissipation Theorems (FDTs), one for each kind of mechanism, are derived and discussed.