Fluctuation relations for anomalous dynamics

TL;DR

This paper investigates fluctuation relations in systems with anomalous diffusion, analyzing how different types of anomalous dynamics affect the validity of fluctuation theorems in nonequilibrium conditions.

Contribution

It extends fluctuation relation analysis to anomalous diffusion processes, combining Langevin and kinetic methods for diverse models.

Findings

Conventional fluctuation relations fail in superdiffusive models without fluctuation-dissipation relation.

Fluctuation relations hold in subdiffusive models with fluctuation-dissipation relation.

The validity of fluctuation relations depends on the type of anomalous dynamics.

Abstract

We consider work fluctuation relations (FRs) for generic types of dynamics generating anomalous diffusion: Levy flights, long-correlated Gaussian processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the probability distributions of mechanical and thermodynamical work in two paradigmatic nonequilibrium situations, respectively: a particle subject to a constant force and a particle in a harmonic potential dragged by a constant force. We check the transient FR for two models exhibiting superdiffusion, where a fluctuation-dissipation relation does not exist, and for two other models displaying subdiffusion, where there is a fluctuation-dissipation relation. In the two former cases the conventional transient FR is not recovered, whereas in the latter two it holds either exactly or in the long-time limit.