Titlebook: Stochastic Systems with Time Delay; Probabilistic and Th Sarah A.M. Loos Book 2021 The Editor(s) (if applicable) and The Author(s), under e

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https://doi.org/10.1007/978-3-030-80771-9Non-Markovian Processes; Time-Delayed Feedback; Stochastic Delay Differential Equations; Fokker-Planck

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Stochastic Thermodynamicsn this scale, individual fluctuating trajectories can transiently violate the second law of thermodynamics, but in the limit of large systems (or long times), one shall always recover the well-established laws of macroscopic thermodynamics.

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The Heat Flow Induced by a Discrete Delay of stochastic energetics [.]. The heat flow and related medium entropy production are key thermodynamic quantities, which already provide important physical insight. They further constitute a nontrivial part of the total entropy production. Based on this consideration, we can already address several fundamental questions.

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Fokker-Planck Equations For Markovian systems, it is well known that Fokker-Planck equations (FPE) provide a complementary way of description, on the .. These are deterministic equations, whose solutions are probability density functions. In the following, we will briefly introduce this concept, first focusing on the Mark