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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:85199 |
| Date | 04 May 2023 |
| Creators | Holubec, Viktor, Ryabov, Artem, Loos, Sarah A.M., Kroy, Klaus |
| Publisher | IOP Publishing |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 1367-2630, 023021 |
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