Theoretical description of effective heat transfer between two viscously coupled beads

TL;DR

This paper provides an analytical framework for understanding heat transfer between two viscously coupled Brownian particles at different temperatures, revealing a fluctuation theorem and asymmetries in energy flux.

Contribution

It introduces an exact fluctuation theorem for energy flux in a system with viscous coupling, applicable in transient states and validated against experimental data.

Findings

Derivation of an exact fluctuation theorem for energy flux.

Identification of asymmetry between hot and cold particles.

Agreement with previous experimental results.

Abstract

We analytically study the role of nonconservative forces, namely viscous couplings, on the statistical properties of the energy flux between two Brownian particles kept at different temperatures. From the dynamical model describing the system, we identify an energy flow that satisfies a fluctuation theorem both in the stationary and in transient states. In particular, for the specific case of a linear nonconservative interaction, we derive an exact fluctuation theorem that holds for any measurement time in the transient regime, and which involves the energy flux alone. Moreover, in this regime the system presents an interesting asymmetry between the hot and cold particles. The theoretical predictions are in good agreement with the experimental results already presented in our previous article [B{\'e}rut et al., Phys. Rev. Lett. 116, 068301 (2016)], where we investigated the thermodynamic properties of two Brownian particles, trapped with optical tweezers, interacting through a dissipative hydrodynamic coupling.