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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Stochastic Thermodynamicss at a generalization of thermodynamic notions towards small-scale systems dominated by thermal fluctuations and towards nonequilibrium systems [.]. On this scale, individual fluctuating trajectories can transiently violate the second law of thermodynamics, but in the limit of large systems (or long

Decimate

Infinite Fokker-Planck Hierarchyderstand the non-Markovian dynamics. Later in Chap. ., we will present a new derivation of the FP description using a Markovian embedding technique [.,.,.,.,.,.]. To better understand the technical and conceptual difference of our approach, we will here also review some earlier work, in particular,

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Approximation for the Two-time Probability density the Fokker-Planck hierarchy. In particular, we have discussed the perturbation theory and the force-linearization closure (Chap. .). While these approaches render quite accurate descriptions of the intrawell dynamics, they do not yield any information about the .-time PDF.

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The Heat Flow Induced by a Discrete Delays with discrete delay. This quantity can be calculated via well-established concepts from stochastic thermodynamics, in particular, from the framework of stochastic energetics [.]. The heat flow and related medium entropy production are key thermodynamic quantities, which already provide important p

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Summaryis a colloidal (Brownian) particle subject to a position-dependent, time-delayed feedback force and nonlinear static forces stemming from a potential. We describe its noisy motion by a Langevin equation, which is, due to the delay, non-local in time and infinite-dimensional.

ensemble

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f structural members. In the contemporary construction landscape, where environmental concerns and resource limitations significantly influence design practices, the integration of sustainability principles into structural engineering has become imperative. The introductory section emphasizes the mu