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: Hardback
Length: 285 pages
Publication date: 19 September 2021
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 of this thesis pertains to the probabilistic description of time-delayed systems. By developing a versatile approximation scheme for nonlinear delay systems, it provides a framework for capturing the intricate dynamics of such systems. This approach enables researchers to gain insights into the behavior of delayed systems and to predict their outcomes with greater accuracy.

Furthermore, the thesis uncovers the intriguing thermodynamic properties that arise when delay is introduced into a system. It demonstrates that delay can lead to the occurrence of anomalous (reversed) heat flow, a phenomenon where heat transfers from a cooler to a warmer region. This discovery expands our understanding of the complex interplay between thermodynamics and time-dependent processes.

Moreover, the thesis showcases how to treat the thermodynamics of non-Markovian systems by introducing auxiliary variables. It reveals that delayed feedback is intricately linked to nonreciprocal coupling, information flow, and net energy input on the fluctuating level. This understanding provides a deeper understanding of the underlying mechanisms driving the nonequilibrium behavior observed in nanoscopic and biological systems.

In conclusion, this thesis makes substantial contributions to the field of nonequilibrium thermodynamics by exploring the behavior of time-delayed systems from a thermodynamic perspective. It provides valuable insights into the probabilistic description of delay-induced phenomena, reveals intriguing thermodynamic properties, and demonstrates how to treat non-Markovian systems using auxiliary variables. These advancements lay the foundation for further research in this dynamic and rapidly evolving field.

Weight: 629g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030807702
Edition number: 1st ed. 2021