Stochastic thermodynamics of Langevin systems under time-delayed feedback control: II. Nonequilibrium steady-state fluctuations

TL;DR

This paper investigates the fluctuations in Langevin systems with time-delayed feedback control, focusing on the steady-state behavior and rare events using a path-integral approach, with applications to harmonic oscillators.

Contribution

It extends previous work by analyzing stochastic fluctuations and rare events in nonequilibrium steady states of delayed feedback Langevin systems.

Findings

Derived analytical expressions for fluctuation statistics.

Numerical validation of theoretical predictions.

Identified the role of rare events in steady-state fluctuations.

Abstract

This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was to derive second-law-like inequalities that provide bounds to the average extracted work. Here we study stochastic fluctuations of time-integrated observables such as the heat exchanged with the environment, the extracted work, or the (apparent) entropy production. We use a path-integral formalism and focus on the long-time behavior in the stationary cooling regime, stressing the role of rare events. This is illustrated by a detailed analytical and numerical study of a Langevin harmonic oscillator driven by a linear feedback.