A Fluctuation-Dissipation Process without Time Scale

TL;DR

This paper investigates how a specific dissipation process affects diffusion driven by long-range correlated fluctuations, leading to non-canonical equilibrium distributions with truncated Levy characteristics.

Contribution

It introduces a dissipation process that alters the equilibrium distribution, showing agreement between theoretical predictions and numerical simulations, and characterizes the resulting non-standard distributions.

Findings

Equilibrium distribution departs from canonical form.

Distribution tails are truncated with sharp peaks.

Central distribution resembles a truncated Levy distribution.

Abstract

We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied numerically and theoretically, with a good agreement between theory and numerical treatment. As a result of this assumption the equilibrium distribution departs from the ordinary canonical distribution. The distribution tails are truncated, the distribution border is signalled by sharp peaks and, in the weak dissipation limit, the central distribution body becomes identical to a truncated Levy distribution.