Entropy reduction from a detailed fluctuation theorem for a nonequilibrium stochastic system driven under feedback control

TL;DR

This paper derives a detailed fluctuation theorem demonstrating how feedback control can reduce entropy in nonequilibrium stochastic systems, allowing for both positive and negative entropy production.

Contribution

It provides a general framework for entropy reduction via feedback control applicable to various types of feedback, extending previous specific studies.

Findings

Entropy reduction is explicitly derived from a detailed fluctuation theorem.

Feedback control can lead to negative entropy production in stochastic systems.

The approach applies to both velocity and position dependent feedback controls.

Abstract

We show explicitly the entropy reduction from a detailed fluctuation theorem for the general stochastic system driven by nonequilibrium process under feedback control. The effect of interaction of the feedback controller with the system is to reduce the entropy of the system. We define the entropy reduction for the single trajectory and show that the overall entropy production for the stochastic system with feedback control can be either positive or negative. The negative entropy production has been studied earlier for a simple system with velocity dependent feedback control [K. H. Kim and H. Qian, Phys. Rev. Lett. {\bf 93}, 120602 (2004)]. Our general approach provides the overall positive or negative entropy production irrespective of velocity dependent and position dependent feedback control.