Non-Poisson Renewal Events and Memory

Abstract

We study two different forms of fluctuation-dissipation processes generating anomalous relaxations to equilibrium of an initial out of equilibrium condition, the former being based on a stationary although very slow correlation function and the latter characterized by the occurrence of crucial events, namely, non-Poisson renewal events, incompatible with the stationary condition. Both forms of regression to equilibrium have the same non-exponential Mittag-Leffler structure. We analyze the single trajectories of the two processes by recording the time distances between two consecutive origin re-crossings and establishing the corresponding waiting time probability density function (PDF), $\psi (t)$. In the former case, with no crucial events, $\psi (t)$ is exponential and in the latter case, with crucial events, $\psi (t)$ is an inverse power law PDF with a diverging first moment. We discuss the consequences that this result is expected to have for the correct interpretation of some anomalous relaxation processes.

13 pages, 7 figures

References in corpus (2)

• Probing microscopic origins of confined subdiffusion by first-passage observables
• Relaxation time distributions for an anomalously diffusing particle