Linear Response and Fluctuation Dissipation Theorem for non-Poissonian Renewal Processes
Disordered Systems and Neural Networks
2009-11-13 v2 Statistical Mechanics
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.
Cite
@article{arxiv.0807.1305,
title = {Linear Response and Fluctuation Dissipation Theorem for non-Poissonian Renewal Processes},
author = {Gerardo Aquino and Paolo Grgolini and Bruce J. West},
journal= {arXiv preprint arXiv:0807.1305},
year = {2009}
}