Partial entropy production in heat transport

TL;DR

This paper investigates the behavior of partial entropy production in a coupled Brownian particle system with heat baths, revealing deviations from the fluctuation theorem when interactions are weak, supported by analytical and numerical analysis.

Contribution

It introduces the concept of partial entropy production in a coupled heat transport system and analyzes deviations from the fluctuation theorem under weak coupling conditions.

Findings

Partial entropy production obeys the fluctuation theorem in the steady state.

Weak interactions cause significant deviations from the fluctuation theorem.

Analytical results are validated through numerical simulations.

Abstract

We consider a system of two Brownian particles (say A and B), coupled to each other via harmonic potential of stiffness constant $k$. Particle-A is connected to two heat baths of constant temperatures $T_1$ and $T_2$, and particle-B is connected to a single heat bath of a constant temperature $T_3$. In the steady state, the total entropy production for both particles obeys the fluctuation theorem. We compute the total entropy production due to one of the particles called as partial or apparent entropy production, in the steady state for a time segment $\tau$. When both particles are weakly interacting with each other, the fluctuation theorem for partial and apparent entropy production is studied. We find a significant deviation from the fluctuation theorem. The analytical results are also verified using numerical simulations.