Equilibrium Stochastic Delay Processes
arXiv:2108.07136 · doi:10.1088/1367-2630/ac4b91
Abstract
Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is available for linear models only. We introduce a class of stochastic delay processes with nonlinear time-local forces and linear time-delayed forces that obey fluctuation theorems and converge to a Boltzmann equilibrium at long times. From the point of view of control theory, such ``equilibrium stochastic delay processes'' are stable and energetically passive, by construction. Computationally, they provide diverse exact constraints on general nonlinear stochastic delay problems and can, in various situations, serve as a starting point for their perturbative analysis. Physically, they admit an interpretation in terms of an underdamped Brownian particle that is either subjected to a time-local force in a non-Markovian thermal bath or to a delayed feedback force in a Markovian thermal bath. We illustrate these properties numerically for a setup familiar from feedback cooling and point out experimental implications.
32 pages, 10 figures, revised
References in corpus (8)
- The 2019 Motile Active Matter Roadmap
- Jarzynski Relation, Fluctuation Theorems, and Stochastic Thermodynamics for Non-Markovian Processes
- Active Brownian Heat Engines
- Stochastic thermodynamics of Langevin systems under time-delayed feedback control: I. Second-law-like inequalities
- Stochastic thermodynamics of Langevin systems under time-delayed feedback control: II. Nonequilibrium steady-state fluctuations
- Uncertainty relations for time-delayed Langevin systems
- Performance and limits of feedback cooling methods for levitated oscillators: a direct comparison
- Optimal control for feedback cooling in cavityless levitated optomechanics