Linear response and Fluctuation-Dissipation Theorem for non-Poissonian renewal processesG. 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
received 19 June 2007; accepted in final form 17 August 2007; published October 2007
published online 17 September 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.
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