Stochastic Systems with Time Delay: Probabilistic and Thermodynamic Descriptions of non-Markovian Processes far From Equilibrium

The nonequilibrium behavior of nanoscopic and biological systems, which are strongly fluctuating, is a major focus of current research. This thesis advances this field by introducing a probabilistic description of time-delayed systems, revealing that delay can induce intriguing thermodynamic properties, and showing how to treat the thermodynamics of non-Markovian systems by introducing auxiliary variables. Delayed feedback is inextricably linked to nonreciprocal coupling, information flow, and net energy input on the fluctuating level.

Format: Paperback / softback
Length: 285 pages
Publication date: 19 September 2022
Publisher: Springer Nature Switzerland AG

The study of nonequilibrium behavior in nanoscopic and biological systems, characterized by significant fluctuations, remains a central focus of ongoing research. In recent years, substantial strides have been made in understanding these complex systems from a thermodynamic perspective. However, the introduction of time delays, such as those caused by feedback loops, presents new theoretical challenges that require further exploration.

This thesis aims to advance this emerging and dynamic field of research in several directions. The first significant contribution lies in the probabilistic description of time-delayed systems. By introducing a versatile approximation scheme for nonlinear delay systems, the thesis provides a valuable tool for analyzing and understanding these systems.

Furthermore, the thesis uncovers intriguing thermodynamic properties that arise due to delay, such as anomalous (reversed) heat flow. It demonstrates how delay can fundamentally alter the thermodynamic behavior of non-Markovian systems, highlighting the importance of considering auxiliary variables to accurately describe and analyze these complex systems.

Delayed feedback emerges as a crucial aspect of the study, as it is intricately linked to nonreciprocal coupling, information flow, and net energy input on the fluctuating level. This research highlights the need for a deeper understanding of the interplay between delay, non-Markovian dynamics, and the overall energy dynamics of these systems.

In conclusion, this thesis contributes to the understanding of nonequilibrium behavior in nanoscopic and biological systems by exploring the effects of time delays and introducing novel approaches to treat non-Markovian systems. It opens up new avenues for research and provides valuable insights into the complex dynamics of these systems, with potential applications in various fields, including nanotechnology, biology, and engineering.

Weight: 474g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030807733
Edition number: 1st ed. 2021