Linear response and Fluctuation-Dissipation Theorem for non-Poissonian renewal processes

¹  Max-Planck-Institut für Physik komplexer Systeme - Nöthnitzer Str. 38, 01187 Dresden, Germany
²  Center for Nonlinear Science, University of North Texas - Denton, TX, USA
³  Dipartimento di Fisica “E. Fermi", Università di Pisa - Largo Pontecorvo, 56127, Pisa, Italy
⁴  Phyics Department, Duke University - Durham, 27708 NC, USA

Corresponding author: gaquino@mpipks-dresden.mpg.de

Received: 19 June 2007
Accepted: 17 August 2007

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 one site to the other but leaves the occurrence times of the attempted jumps (“events") unchanged 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.