Entropy production and fluctuation theorems under feedback control: the molecular refrigerator model revisited

TL;DR

This paper analyzes a feedback-controlled Brownian particle model, exploring entropy production fluctuations and fluctuation theorems, with explicit solutions for a harmonic oscillator illustrating the complex interplay of boundary and bulk effects.

Contribution

It provides a detailed analysis of entropy fluctuations under feedback control, revealing differences in forward and backward dynamics and deriving explicit solutions for a harmonic oscillator.

Findings

Explicit fluctuation theorem involves different dynamics in forward and backward processes

Characteristic function of entropy production calculated for a harmonic oscillator

Large deviation function shows interplay between boundary and bulk contributions

Abstract

We revisit the model of a Brownian particle in a heat bath submitted to an actively controlled force proportional to the velocity that leads to thermal noise reduction (cold damping). We investigate the influence of the continuous feedback on the fluctuations of the total entropy production and show that the explicit expression of the detailed fluctuation theorem involves different dynamics and observables in the forward and backward processes. As an illustration, we study the analytically solvable case of a harmonic oscillator and calculate the characteristic function of the entropy production in a nonequilibrium steady state. We then determine the corresponding large deviation function which results from an unusual interplay between 'boundary' and 'bulk' contributions.