A generalized fluctuation relation for power-law distributions

TL;DR

This paper introduces a new fluctuation relation symmetry suitable for power-law distributions in nonequilibrium systems, addressing violations of traditional theorems and applying it to complex environments and Lévy noise scenarios.

Contribution

It proposes an alternative fluctuation relation symmetry that is monotonic and linear in the power-law regime, consistent with a large deviation-like principle, and demonstrates its application to complex systems.

Findings

The new fluctuation relation is monotonic and linear for power-law distributions.

It applies to systems with spatiotemporal temperature fluctuations and Lévy noise.

The fluctuation relation depends solely on the average bath temperature.

Abstract

Strong violations of existing fluctuation theorems may arise in nonequilibrium steady states characterized by distributions with power-law tails. The ratio of the probabilities of positive and negative fluctuations of equal magnitude behaves in an anomalous nonmonotonic way [H. Touchette and E.G.D. Cohen, Phys. Rev. E \textbf{76}, 020101(R) (2007)]. Here, we propose an alternative definition of fluctuation relation (FR) symmetry that, in the power-law regime, is characterized by a monotonic linear behavior. The proposal is consistent with a large deviation-like principle. As example, it is studied the fluctuations of the work done on a dragged particle immersed in a complex environment able to induce power-law tails. When the environment is characterized by spatiotemporal temperature fluctuations, distributions arising in nonextensive statistical mechanics define the work statistics. In that situation, we find that the FR symmetry is solely defined by the average bath temperature. The case of a dragged particle subjected to a L\'{e}vy noise is also analyzed in detail.