Volume 80, Number 1, October 2007
|Number of page(s)||6|
|Published online||17 September 2007|
Linear response and Fluctuation-Dissipation Theorem for non-Poissonian renewal processes
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: email@example.com
Accepted: 17 August 2007
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.
PACS: 05.20.-y – Classical statistical mechanics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.60.-k – Transport processes
© Europhysics Letters Association, 2007
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