Heat and work distributions for mixed Gauss-Cauchy process

TL;DR

This paper investigates the energetics of a non-Gaussian Langevin process driven by independent Gaussian and Cauchy noises, analyzing heat and work distributions in a nonequilibrium setting.

Contribution

It introduces a framework for defining thermodynamic quantities for non-Gaussian stochastic processes with Levy noise, focusing on heat and work distributions.

Findings

Derived heat and work distribution formulas for mixed Gauss-Cauchy processes.

Analyzed the impact of Cauchy fluctuations on energy dissipation and work.

Provided insights into non-Gaussian fluctuation effects in nonequilibrium systems.

Abstract

We analyze energetics of a non-Gaussian process described by a stochastic differential equation of the Langevin type. The process represents a paradigmatic model of a nonequilibrium system subject to thermal fluctuations and additional external noise, with both sources of perturbations considered as additive and statistically independent forcings. We define thermodynamic quantities for trajectories of the process and analyze contributions to mechanical work and heat. As a working example we consider a particle subjected to a drag force and two independent Levy white noises with stability indices $\alpha=2$ and $\alpha=1$. The fluctuations of dissipated energy (heat) and distribution of work performed by the force acting on the system are addressed by examining contributions of Cauchy fluctuations to either bath or external force acting on the system.