Linear response and fluctuation-dissipation theorem for non-poissonian renewal processes

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. Copyright (C) EPLA, 2007.