Fluctuation relation for a L\'evy particle

TL;DR

This paper investigates work fluctuations of a particle driven by deterministic and Lévy-stable random forces, revealing power-law tails in work distribution that violate traditional fluctuation theorems and suggest new experimental tests.

Contribution

It introduces a novel analysis of work fluctuations under Lévy noise, showing non-monotonic probability ratios and deviations from classical fluctuation relations.

Findings

Work distribution exhibits fat power-law tails.

Traditional fluctuation theorems are violated.

Probability ratio of work fluctuations is non-monotonic.

Abstract

We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the L\'evy type. In the stationary regime, the probability density of the work is found to have ``fat'' power-law tails which assign a relatively high probability to large fluctuations compared with the case where the random forcing is Gaussian. These tails lead to a strong violation of existing fluctuation theorems, as the ratio of the probabilities of positive and negative work fluctuations of equal magnitude behaves in a non-monotonic way. Possible experiments that could probe these features are proposed.