Fluctuation-dissipation relations under Levy noises

TL;DR

This paper explores how the fluctuation-dissipation theorem (FDT) can be extended to systems driven far from equilibrium by analyzing a model with Levy noise and time-dependent forces, revealing conditions for FDT validity.

Contribution

It demonstrates the application of generalized FDT to systems influenced by Levy stable noises and deterministic forces, extending the understanding of fluctuation-response relations far from equilibrium.

Findings

FDT can be restored in Levy noise-driven systems with appropriate variable choices

The response functions are derived for systems under alpha-stable noise

Conditions under which FDT holds far from equilibrium are identified

Abstract

For systems close to equilibrium, the relaxation properties of measurable physical quantities are described by the linear response theory and the fluctuation-dissipation theorem (FDT). Accordingly, the response or the generalized susceptibility, which is a function of the unperturbed equilibrium system, can be related to the correlation between spontaneous fluctuations of a given conjugate variable. There have been several attempts to extend the FDT far from equilibrium, introducing new terms or using effective temperatures. Recently, Prost, Joanny, and Parrondo [Phys. Rev. Lett. 103, 090601 (2009)] have shown that the FDT can be restored far from equilibrium by choosing the appropriate variables conjugate to the external perturbations. Here, we apply the generalized FDT to a system perturbed by time-dependent deterministic forces and acting under the influence of white alpha-stable noises.