This book has a long history of more than 20 years. The first attempt to write a monograph on information-theoretic approach to thermodynamics was done by one of the authors (RSI) in 1974 when he published, in the preprint form, two volumes of the book "Information Theory and Thermodynamics" concerning classical and quantum information theory, [153] (220 pp.), [154] (185 pp.). In spite of the encouraging remarks by some of the readers, the physical part of this book was never written except for the first chapter. Now this material is written completely anew and in much greater extent. A few years earlier, in 1970, second author of the present book, (AK), a doctoral student and collaborator of RSI in Toruli, published in Polish, also as a preprint, his habilitation dissertation "Information-theoretical decision scheme in quantum statistical mechanics" [196] (96 pp.). This small monograph presented his original results in the physical part of the theory developed in the Torun school. Unfortunately, this preprint was never published in English. The present book contains all these results in a much more modern and developed form.

This book aims to present an information-theoretical approach to thermodynamics and its generalisations. On the one hand, it generalises the concept of `information thermodynamics' to that of `information dynamics' in order to stress applications outside thermal phenomena. On the other hand, it is a synthesis of the dynamics of state change and the theory of complexity, which provide a common framework to treat both physical and nonphysical systems together. Both classical and quantum systems are discussed, and two appendices are included to explain principal definitions and some important aspects of the theory of Hilbert spaces and operator algebras. The concept of higher-order temperatures is explained and applied to biological and linguistic systems. The theory of open systems is presented in a new, much more general form. Audience: This volume is intended mainly for theoretical and mathematical physicists, but also for mathematicians, experimental physicists, physical chemists, theoretical biologists, communication engineers, and all those interested in entropy and open systems. It can also be recommended as a supplementary text.

This book discusses the elementary ideas and tools needed for open quantum systems in a comprehensive manner. The emphasis is given to both the traditional master equation as well as the functional (path) integral approaches. It discusses the basic paradigm of open systems, the harmonic oscillator and the two-level system in detail. The traditional topics of dissipation and tunneling, as well as the modern field of quantum information, find a prominent place in the book. Assuming a basic background of quantum and statistical mechanics, this book will help readers familiarize with the basic tools of open quantum systems. Open quantum systems is the study of quantum dynamics of the system of interest, taking into account the effects of the ambient environment. It is ubiquitous in the sense that any system could be envisaged to be surrounded by its environment which could naturally exert its influence on it. Open quantum systems allows for a systematic understanding of irreversible processes such as decoherence and dissipation, of the essence in order to have a correct understanding of realistic quantum dynamics and also for possible implementations. This would be essential for a possible development of quantum technologies.

In this book we develop various mathematical models of information dynamics, I -dynamics (including the process of thinking), based on methods of classical and quantum physics. The main aim of our investigations is to describe mathematically the phenomenon of consciousness. We would like to realize a kind of Newton-Descartes program (corrected by the lessons of statistical and quantum mechanics) for information processes. Starting from the ideas of Newton and Descartes, in physics there was developed an adequate description of the dynamics of material systems. We would like to develop an analogous mathematical formalism for information and, in particular, mental processes. At the beginning of the 21st century it is clear that it would be impossible to create a deterministic model for general information processes. A deterministic model has to be completed by a corresponding statistical model of information flows and, in particular, flows of minds. It might be that such an information statistical model should have a quantum-like structure.

This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented. The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.

The nature of distributed computation in complex systems has often been described in terms of memory, communication and processing. This thesis presents a complete information-theoretic framework to quantify these operations on information (i.e. information storage, transfer and modification), and in particular their dynamics in space and time. The framework is applied to cellular automata, and delivers important insights into the fundamental nature of distributed computation and the dynamics of complex systems (e.g. that gliders are dominant information transfer agents). Applications to several important network models, including random Boolean networks, suggest that the capability for information storage and coherent transfer are maximised near the critical regime in certain order-chaos phase transitions. Further applications to study and design information structure in the contexts of computational neuroscience and guided self-organisation underline the practical utility of the techniques presented here.

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This volume seeks to return to the starting point of bio-informatics and quantum information, where these fields are constantly engaged in explosive advancements, and to seriously attempt mutual interaction between the two fields, with a view to enumerating and solving the many encountered fundamental problems. For such a purpose, we look for interdisciplinary bridges in mathematics, physics, information and life sciences, in particular, the research for a new paradigm for information science and life science on the basis of quantum theory.

This volume includes papers by leading mathematicians in the fields of stochastic analysis, white noise theory and quantum information, together with their applications. The papers selected were presented at the International Conference on Stochastic Analysis: Classical and Quantum held at Meijo University, Nagoya, Japan from 1 to 5 November 2004. The large range of subjects covers the latest research in probability theory.

"The Winter School and the International Conference on 'Quantum Information and Complexity' was held from 6 to 10 January 2003, at Meijo University, Nagoya"--P. v.