Nonequilibrium fluctuation theorem for systems under discrete and continuous feedback control

TL;DR

This paper derives a fluctuation theorem for nonequilibrium systems with feedback control, accounting for entropy production from measurements, and verifies it through calculations and simulations.

Contribution

It introduces a fluctuation theorem that includes measurement-induced entropy production in feedback-controlled stochastic systems.

Findings

The total entropy production satisfies an integrated fluctuation theorem.

The fluctuation theorem is verified through explicit calculations.

Simulations confirm the theoretical predictions.

Abstract

Without violating causality, we allow performing measurements in time reverse process of a feedback manipulated stochastic system. As a result we come across an entropy production due to the measurement process. This entropy production, in addition to the usual system and medium entropy production, constitutes the total entropy roduction of the combined system of the reservoir, the system and the feedback controller. We show that this total entropy production of "full" system satisfies an integrated fluctuation theorem as well as a detailed fluctuation theorem as expected. We illustrate and verify this idea through explicit calculation and direct simulation in two examples.