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

摘要

This paper is the second in a series devoted to the study of Langevin systems subjected to a continuoustime-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was toderive second-law-like inequalities that provide bounds to the average extracted work. Here we study stochasticfluctuations 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 inthe stationary cooling regime, stressing the role of rare events. This is illustrated by a detailed analytical andnumerical study of a Langevin harmonic oscillator driven by a linear feedback.