Ebook: Statistical Theory of Open Systems: Volume 1: A Unified Approach to Kinetic Description of Processes in Active Systems

Let us begin by quoting from the Preface to the author's Statistical Physics (Moscow, Nauka 1982; also published in English by Harwood in 1986): '''My God! Yet another book on statistical physics! There's no room on my bookshelves left!' Such emotionsare quite understandable. Beforejumping to conclusions, however, it would be worthwhile to read the Introduction and look through the table of contents. Then the reader will find that this book is totally different from the existing courses, fundamental and concise. ... We do not use the conventional division into statistical theories ofequilibrium and nonequilibrium states. Rather than that, the theory ofnonequilibrium state is the basis and the backbone oftheentirecourse. ... This approach allows us to develop a unified method for statistical description ofa very broadclassofsystems. ... The author certainly does not wish to exaggerate the advantages of the book, considering it asjustthe first attemptto create a textbookofa new kind." The next step in this direction was the author's Turbulent Motion and the Structure of Chaos (Moscow, Nauka 1990; Kluwer Academic Publishers 1991). This book is subtitled A New Approach to the Statistical Theory of Open Systems. Naturally, the "new approach" is not meant to defy the consistent and efficient methods of the conventional statistical theory; itshould be regarded as auseful reinforcementofsuch methods.

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This monograph gives a systematic presentation of ideas, methods and results of the modern statistical theory of open systems -- systems capable of exchanging matter, energy and information with the surrounding world. The resulting self-organization can lead to more sophisticated and advanced structures.
Central to this work are the statistical criteria of self-organization. The feasibility of a unified description of kinetic, hydrodynamic and diffusion processes in passive and active macroscopic systems without resorting to the methods of perturbation theory is demonstrated. On this basis, a general definition of thermal flux is given in terms of the entropy gradient. Moreover, a consistent method for calculating both kinetic and hydrodynamic fluctuations is proposed. This approach is then used to construct a theory of classical and anomalous Brownian motion in nonlinear media.
This theory makes it possible to treat in an original way the phenomenon of turbulence, and to propose a unified kinetic description of laminar and turbulent motion. The proposed methods are also applied to the statistical description of quantum macroscopic open systems. This provides answers as to whether or not the quantum mechanical description is complete, and whether or not there are hidden parameters in quantum mechanics. The book has no analogy in the existing literature. It is both a monograph and a textbook, and is based largely on the author's original research.
The book will be useful to postgraduate students and researchers in chemistry, physics, mathematics, economics, sociology, and engineering.

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This monograph gives a systematic presentation of ideas, methods and results of the modern statistical theory of open systems -- systems capable of exchanging matter, energy and information with the surrounding world. The resulting self-organization can lead to more sophisticated and advanced structures.
Central to this work are the statistical criteria of self-organization. The feasibility of a unified description of kinetic, hydrodynamic and diffusion processes in passive and active macroscopic systems without resorting to the methods of perturbation theory is demonstrated. On this basis, a general definition of thermal flux is given in terms of the entropy gradient. Moreover, a consistent method for calculating both kinetic and hydrodynamic fluctuations is proposed. This approach is then used to construct a theory of classical and anomalous Brownian motion in nonlinear media.
This theory makes it possible to treat in an original way the phenomenon of turbulence, and to propose a unified kinetic description of laminar and turbulent motion. The proposed methods are also applied to the statistical description of quantum macroscopic open systems. This provides answers as to whether or not the quantum mechanical description is complete, and whether or not there are hidden parameters in quantum mechanics. The book has no analogy in the existing literature. It is both a monograph and a textbook, and is based largely on the author's original research.
The book will be useful to postgraduate students and researchers in chemistry, physics, mathematics, economics, sociology, and engineering.

Content:
Front Matter....Pages i-xv
Introduction....Pages 1-34
Dynamic and Statistical Description of Processes in Macroscopic Systems....Pages 35-46
Statistical Theory of Equilibrium State....Pages 47-67
Distributions of Functions of Dynamic Variables. Fluctuations of Internal Parameters....Pages 68-87
Methods of Distribution Functions and Microscopic Phase Density....Pages 88-101
Boltzmann Kinetic Equation....Pages 102-116
From BBGKY Equations to Kinetic Equations for Boltzmann Gas....Pages 117-129
Kinetic Theory of Nonideal Gas....Pages 130-141
Kinetic Theory of Fluctuations....Pages 142-158
Langevin Method in Kinetic Theory of Fluctuations....Pages 159-171
From Kinetic Boltzmann Equation to Equations of Gas Dynamics....Pages 172-187
Thermodynamics of Nonequilibrium Irreversible Processes....Pages 188-212
Unified Description of Kinetic and Hydrodynamic Processes....Pages 213-234
Transition from Generalized Kinetic Equation to Equations of Gas Dynamics....Pages 235-257
Nonlinear Brownian Motion....Pages 258-299
Examples of Nonlinear Brownian Motion....Pages 300-334
Nonlinear Brownian Motion. Unified Description of Kinetic, Hydrodynamic and Diffusion Processes....Pages 335-360
Kinetic Theory of Active Media....Pages 361-386
Kinetic Theory of Fluctuations in Active Media....Pages 387-420
Anomalous Brownian Motion. Equilibrium and Nonequilibrium Natural Flicker Noise and Residual Time Correlations....Pages 421-449
Criteria of Self-Organization....Pages 450-482
Turbulent Motion. Kinetic Description of Turbulence....Pages 483-524
Bridge from Classical Statistical Theory of Open Systems to Quantum Theory....Pages 525-554
Conclusion....Pages 555-556
Back Matter....Pages 557-574

---

This monograph gives a systematic presentation of ideas, methods and results of the modern statistical theory of open systems -- systems capable of exchanging matter, energy and information with the surrounding world. The resulting self-organization can lead to more sophisticated and advanced structures.
Central to this work are the statistical criteria of self-organization. The feasibility of a unified description of kinetic, hydrodynamic and diffusion processes in passive and active macroscopic systems without resorting to the methods of perturbation theory is demonstrated. On this basis, a general definition of thermal flux is given in terms of the entropy gradient. Moreover, a consistent method for calculating both kinetic and hydrodynamic fluctuations is proposed. This approach is then used to construct a theory of classical and anomalous Brownian motion in nonlinear media.
This theory makes it possible to treat in an original way the phenomenon of turbulence, and to propose a unified kinetic description of laminar and turbulent motion. The proposed methods are also applied to the statistical description of quantum macroscopic open systems. This provides answers as to whether or not the quantum mechanical description is complete, and whether or not there are hidden parameters in quantum mechanics. The book has no analogy in the existing literature. It is both a monograph and a textbook, and is based largely on the author's original research.
The book will be useful to postgraduate students and researchers in chemistry, physics, mathematics, economics, sociology, and engineering.

Content:
Front Matter....Pages i-xv
Introduction....Pages 1-34
Dynamic and Statistical Description of Processes in Macroscopic Systems....Pages 35-46
Statistical Theory of Equilibrium State....Pages 47-67
Distributions of Functions of Dynamic Variables. Fluctuations of Internal Parameters....Pages 68-87
Methods of Distribution Functions and Microscopic Phase Density....Pages 88-101
Boltzmann Kinetic Equation....Pages 102-116
From BBGKY Equations to Kinetic Equations for Boltzmann Gas....Pages 117-129
Kinetic Theory of Nonideal Gas....Pages 130-141
Kinetic Theory of Fluctuations....Pages 142-158
Langevin Method in Kinetic Theory of Fluctuations....Pages 159-171
From Kinetic Boltzmann Equation to Equations of Gas Dynamics....Pages 172-187
Thermodynamics of Nonequilibrium Irreversible Processes....Pages 188-212
Unified Description of Kinetic and Hydrodynamic Processes....Pages 213-234
Transition from Generalized Kinetic Equation to Equations of Gas Dynamics....Pages 235-257
Nonlinear Brownian Motion....Pages 258-299
Examples of Nonlinear Brownian Motion....Pages 300-334
Nonlinear Brownian Motion. Unified Description of Kinetic, Hydrodynamic and Diffusion Processes....Pages 335-360
Kinetic Theory of Active Media....Pages 361-386
Kinetic Theory of Fluctuations in Active Media....Pages 387-420
Anomalous Brownian Motion. Equilibrium and Nonequilibrium Natural Flicker Noise and Residual Time Correlations....Pages 421-449
Criteria of Self-Organization....Pages 450-482
Turbulent Motion. Kinetic Description of Turbulence....Pages 483-524
Bridge from Classical Statistical Theory of Open Systems to Quantum Theory....Pages 525-554
Conclusion....Pages 555-556
Back Matter....Pages 557-574
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