Related Experiment Video
Updated: Mar 6, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Stochastic thermodynamics of Langevin systems under time-delayed feedback control. II. Nonequilibrium steady-state
M L Rosinberg1, G Tarjus1, T Munakata2
1Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRS UMR 7600, 4 place Jussieu, 75252 Paris Cedex 05, France.
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)PLEEE81539-375510.1103/PhysRevE.91.042114] 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.
Related Concept Videos
Feedback control systems
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Second Order systems II
Transient and Steady-state Response
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state...
Linear time-invariant Systems
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
Time and frequency -Domain Interpretation of Phase-lag Control
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

