This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems, electromagnetics, statistical signal processing, quantum information theory, quantum neural network theory, quantum filtering theory, quantum electrodynamics, quantum general relativity, string theory, problems in biology and classical and quantum fluid dynamics. The selection of the problems has been based on courses taught by the author to undergraduates and postgraduates in Electronics and Communications Engineering. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

Since their first introduction in natural sciences through the work of Einstein on Brownian motion in 1905 and further works, in particular by Langevin, Smoluchowski and others, stochastic processes have been used in several areas of science and technology. For example, they have been applied in chemical studies, or in fluid turbulence and for combustion and reactive flows. The articles in this book provide a general and unified framework in which stochastic processes are presented as modeling tools for various issues in engineering, physics and chemistry, with particular focus on fluid mechanics and notably dispersed two-phase flows. The aim is to develop what can referred to as stochastic modeling for a whole range of applications.

The theory of thermodynamics has been one of the bedrocks of 19th-century physics, and thermodynamic problems have inspired Planck's quantum hypothesis. One hundred years later, in an era where we design increasingly sophisticated nanotechnologies, researchers in quantum physics have been 'returning to their roots', attempting to reconcile modern nanoscale devices with the theory of thermodynamics. This textbook explains how it is possible to unify the two opposite pictures of microscopic quantum physics and macroscopic thermodynamics in one consistent framework, proving that the ancient theory of thermodynamics still offers many remarkable insights into present-day problems. This textbook focuses on the microscopic derivation and understanding of key principles and concepts and their interrelation. The topics covered in this book include (quantum) stochastic processes, (quantum) master equations, local detailed balance, classical stochastic thermodynamics, (quantum) fluctuation theorems, strong coupling and non-Markovian effects, thermodynamic uncertainty relations, operational approaches, Maxwell's demon, and time-reversal symmetry, among other topics. The textbook also explores several practical applications of the theory in more detail, including single-molecule pulling experiments, quantum transport and thermoelectric effects in quantum dots, the micromaser, and related setups in quantum optics. The aim of this book is to inspire readers to investigate a plethora of modern nanoscale devices from a thermodynamic point of view, allowing them to address their dissipation, efficiency, reliability, and power based on a conceptually clear understanding about the microscopic origin of heat, entropy, and the second law. The book is accessible to graduate students, post-docs, and lecturers, but will also be of interest to all researchers striving for a deeper understanding of the laws of thermodynamics beyond their traditional realm of applicability.

This book provides a systematic, self-contained treatment of the theory of quantum probability and quantum Markov processes for graduate students and researchers. Building a framework that parallels the development of classical probability, it aims to help readers up the steep learning curve of the quantum theory.

This new edition of Van Kampen's standard work has been completely revised and updated. Three major changes have also been made. The Langevin equation receives more attention in a separate chapter in which non-Gaussian and colored noise are introduced. Another additional chapter contains old and new material on first-passage times and related subjects which lay the foundation for the chapter on unstable systems. Finally a completely new chapter has been written on the quantum mechanical foundations of noise. The references have also been expanded and updated.

This collection of selected reprints presents as broad a selection as possible, emphasizing formal and numerical aspects of Stochastic Quantization. It reviews and explains the most important concepts placing selected reprints and crucial papers into perspective and compact form.

This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920''s, corresponding to a sum over random trajectories, anticipating by two decades Feynman''s famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950''s. The last quarter of the 20th century has witnessed a growing interest in this technique and its application in several branches of research, even outside physics (for instance, in economy).The aim of this book is to offer a brief but complete presentation of the path integral approach to stochastic processes. It could be used as an advanced textbook for graduate students and even ambitious undergraduates in physics. It describes how to apply these techniques for both Markov and non-Markov processes. The path expansion (or semiclassical approximation) is discussed and adapted to the stochastic context. Also, some examples of nonlinear transformations and some applications are discussed, as well as examples of rather unusual applications. An extensive bibliography is included. The book is detailed enough to capture the interest of the curious reader, and complete enough to provide a solid background to explore the research literature and start exploiting the learned material in real situations.

We introduce the theory of chemical reaction networks and their relation to stochastic Petri nets — important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results concerning chemical reaction networks and Petri nets.

The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

Provides engineers with the knowledge they need to apply thermodynamics and solve engineering challenges at the molecular level.