Energy exchanges in a damped Langevin-like system with two thermal baths and an athermal reservoir

TL;DR

This paper analyzes a Langevin-like system with two thermal baths and an athermal reservoir, deriving exact expressions for energy exchange statistics and revealing complex dependencies on athermal noise properties.

Contribution

It provides an exact calculation of the cumulant-generating function for a system with combined thermal and athermal noise sources, highlighting new energy exchange behaviors.

Findings

Exact cumulant-generating function derived

Long-time energy injection and heat exchange characterized

Covariance of heat shows complex dependence on athermal noise

Abstract

We study a Langevin-like model which describes an inertial particle in a one-dimensional harmonic potential and subjected to two heat baths and one athermal environment. The thermal noises are white and Gaussian, and the temperatures of heat reservoirs are different. The athermal medium act through an external non-Gaussian noise of Poisson type. We calculate exactly the time-dependent cumulant-generating function of position and velocity of the particle, as well as an expression of this generating function for stationary states. We discuss the long-time behavior of first cumulants of the energy injected by the athermal reservoir and the heat exchanged with thermal baths. In particular, we find that the covariance of stochastic heat due to distinct thermal baths exhibits a complex dependence on properties of athermal noise.