Stochastic Systems with Time Delay: Probabilistic and Thermodynamic Descriptions of non-Markovian Pr

Sarah A.M. Loos - Collection Yellow Sale 2023

285 pages, parution le 18/09/2021

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Résumé

The nonequilibrium behavior of nanoscopic and biological systems, which are typically strongly fluctuating, is a major focus of current research. However, new theoretical challenges emerge when the fluctuating system is additionally subject to time delay, e.g. by introducing a versatile approximation scheme for nonlinear delay systems.The nonequilibrium behavior of nanoscopic and biological systems, which are typically strongly fluctuating, is a major focus of current research. Lately, much progress has been made in understanding such systems from a thermodynamic perspective. However, new theoretical challenges emerge when the fluctuating system is additionally subject to time delay, e.g. due to the presence of feedback loops. This thesis advances this young and vibrant research field in several directions. The first main contribution concerns the probabilistic description of time-delayed systems; e.g. by introducing a versatile approximation scheme for nonlinear delay systems. Second, it reveals that delay can induce intriguing thermodynamic properties such as anomalous (reversed) heat flow. More generally, the thesis shows how to treat the thermodynamics of non-Markovian systems by introducing auxiliary variables. It turns out that delayed feedback is inextricably linked to nonreciprocal coupling, information flow, and to net energy input on the fluctuating level.The Langevin Equation.- Fokker-Planck Equations.- Stochastic Thermodynamics.- Infinite Fokker-Planck Hierarchy.- A Markovian Embedding - New Derivation of the Fokker-Planck Hierarchy.
Sarah Loos studied physics at Saarland University and Technical University Berlin, and spent one semester at Duke University in North Carolina, USA. She wrote her multi-award winning PhD thesis at Technical University Berlin and is now a Postdoc at Leipzig University. During her early career, Loos published numerous research articles and contributed to book chapters in the fields of nonlinear dynamics and statistical physics. Besides research activities she engages in science communication.