Anomalous fluctuation relations

TL;DR

This paper investigates fluctuation relations in nonequilibrium systems driven by Lévy noise, revealing anomalous relations for certain noise parameters and connecting them to large deviation theory, with potential experimental implications.

Contribution

It extends previous work by analyzing fluctuation relations under Lévy noise, identifying conditions for anomalous versus conventional fluctuation relations, and discussing their theoretical and experimental significance.

Findings

For 0<μ<2, distributions satisfy anomalous fluctuation relations with symmetric probabilities.

At μ=2, distributions follow conventional fluctuation relations with exponential asymmetry.

The paper discusses the large deviation theory context and experimental prospects for observing these relations.

Abstract

We complement and extend our work on fluctuation relations arising in nonequilibrium systems in steady states driven by L\'evy noise [Phys. Rev. E 76, 020101(R) (2006)]. As a concrete example, we consider a particle subjected to a drag force and a L\'evy white noise with tail index $\mu\in (0,2]$, and calculate the probability distribution of the work done on the particle by the drag force, as well as the probability distribution of the work dissipated by the dragged particle in a nonequilibrium steady state. For $0<\mu<2$, both distributions satisfy what we call an anomalous fluctuation relation, characterized by positive and negative fluctuations that asymptotically have the same probability. For $\mu=2$, by contrast, the work and dissipated work distributions satisfy the known conventional and extended fluctuation relations, respectively, which are both characterized by positive fluctuations that are exponentially more probable than negative fluctuations. The difference between these different fluctuation relations is discussed in the context of large deviation theory. Experiments that could probe or reveal anomalous fluctuation relations are also discussed.