Statistical features of systems driven by non-Gaussian processes: theory & practice

TL;DR

This paper investigates the statistical properties of non-equilibrium systems driven by non-Gaussian noise, providing analytical tools and empirical methods to characterize entropy production and time-reversal symmetry breaking.

Contribution

It introduces a theoretical framework for analyzing Langevin systems with mixed Gaussian and Poissonian noise, including new expressions for entropy production and a scale-dependent inference method.

Findings

Detailed balance does not hold despite symmetric correlation functions.

Entropy production can be non-zero even with zero currents.

A modified Brownian gyrator acts as a two-dimensional linear ratchet.

Abstract

Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here we consider a class of Markov processes described by Langevin equations driven by a mixture of Gaussian and Poissonian noises, focusing on their non-equilibrium properties. In particular, we prove that detailed balance does not hold even when correlation functions are symmetric under time reversal. In such cases, a breakdown of the time reversal symmetry can be highlighted by considering higher order correlation functions. Furthermore, the entropy production may be different from zero even for vanishing currents. We provide analytical expressions for the average entropy production rate in several cases. We also introduce a scale dependent estimate for entropy production, suitable for inference from experimental signals. The empirical entropy production allows us to discuss the role of spatial and temporal resolutions in characterizing non-equilibrium features. Finally, we revisit the Brownian gyrator introducing an additional Poissonian noise showing that it behaves as a two dimensional linear ratchet. It has also the property that when Onsager relations are satisfied its entropy production is positive although it is minimal. We conclude discussing estimates of entropy production for partially accessible systems, comparing our results with the lower bound provided by the thermodynamic uncertainty relations.