Issue
EPL
Volume 80, Number 1, October 2007
Article Number 10002
Number of page(s) 6
Section General
DOI http://dx.doi.org/10.1209/0295-5075/80/10002
Published online 17 September 2007
EPL, 80 (2007) 10002
DOI: 10.1209/0295-5075/80/10002

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

G. Aquino1, P. Grigolini2, 3 and B. J. West4

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

gaquino@mpipks-dresden.mpg.de

received 19 June 2007; accepted in final form 17 August 2007; published October 2007
published online 17 September 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.

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