Anomalous fluctuation relations

TL;DR

This paper investigates how fluctuation relations, which describe the probabilities of work fluctuations in nonequilibrium systems, are modified in anomalous diffusive systems like Levy flights and fractional kinetics.

Contribution

It introduces a new framework for understanding fluctuation relations in anomalous diffusion, extending the classical FRs to non-Brownian dynamics.

Findings

Derived new forms of fluctuation relations for anomalous diffusion.

Linked fluctuation relations to fluctuation-dissipation theorem validity.

Applied results to biological cell migration dynamics.

Abstract

We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the sense that the diffusive properties strongly deviate from the ones of standard Brownian motion. We first briefly review the concept of transient work FRs for stochastic dynamics modeled by the ordinary Langevin equation. We then introduce three generic types of dynamics generating anomalous diffusion: L\'evy flights, long-time correlated Gaussian stochastic processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the work probability distributions in the simple nonequilibrium situation of a particle subject to a constant force. This allows us to check the transient FR for anomalous dynamics. We find a new form of FRs, which is intimately related to the validity of fluctuation-dissipation relations. Analogous results are obtained for a particle in a harmonic potential dragged by a constant force. We argue that these findings are important for understanding fluctuations in experimentally accessible systems. As an example, we discuss the anomalous dynamics of biological cell migration both in equilibrium and in nonequilibrium under chemical gradients.