[PDF] An Introduction To Chaos In Nonequilibrium Statistical Mechanics eBook

Author : J. R. Dorfman
Publisher : Cambridge University Press
Page : 303 pages
File Size : 32,74 MB
Release : 1999-08-28
Category : Science
ISBN : 0521655897

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Introduction to applications and techniques in non-equilibrium statistical mechanics of chaotic dynamics.

Author : Rainer Klages
Publisher : World Scientific
Page : 458 pages
File Size : 33,4 MB
Release : 2007
Category : Science
ISBN : 9812565078

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A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory.Understanding macroscopic properties of matter starting from microscopic chaos in the equations of motion of single atoms or molecules is a key problem in nonequilibrium statistical mechanics. Of particular interest both for theory and applications are transport processes such as diffusion, reaction, conduction and viscosity.Recent advances towards a deterministic theory of nonequilibrium statistical physics are summarized: Both Hamiltonian dynamical systems under nonequilibrium boundary conditions and non-Hamiltonian modelings of nonequilibrium steady states by using thermal reservoirs are considered. The surprising new results include transport coefficients that are fractal functions of control parameters, fundamental relations between transport coefficients and chaos quantities, and an understanding of nonequilibrium entropy production in terms of fractal measures and attractors.The theory is particularly useful for the description of many-particle systems with properties in-between conventional thermodynamics and nonlinear science, as they are frequently encountered on nanoscales.

Author : Pierre Gaspard
Publisher : Cambridge University Press
Page : 496 pages
File Size : 31,34 MB
Release : 2005-07-21
Category : Science
ISBN : 9780521018258

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This book describes recent advances in the application of chaos theory to classical scattering and nonequilibrium statistical mechanics generally, and to transport by deterministic diffusion in particular. The author presents the basic tools of dynamical systems theory, such as dynamical instability, topological analysis, periodic-orbit methods, Liouvillian dynamics, dynamical randomness and large-deviation formalism. These tools are applied to chaotic scattering and to transport in systems near equilibrium and maintained out of equilibrium. This book will be bought by researchers interested in chaos, dynamical systems, chaotic scattering, and statistical mechanics in theoretical, computational and mathematical physics and also in theoretical chemistry.

Author : Pierre Gaspard
Publisher : Cambridge University Press
Page : 496 pages
File Size : 46,42 MB
Release : 1998-05-21
Category : Science
ISBN : 9780521395113

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This book describes recent advances in the application of chaos theory to classical scattering and nonequilibrium statistical mechanics generally, and to transport by deterministic diffusion in particular. The author presents the basic tools of dynamical systems theory, such as dynamical instability, topological analysis, periodic-orbit methods, Liouvillian dynamics, dynamical randomness and large-deviation formalism. These tools are applied to chaotic scattering and to transport in systems near equilibrium and maintained out of equilibrium. This book will be bought by researchers interested in chaos, dynamical systems, chaotic scattering, and statistical mechanics in theoretical, computational and mathematical physics and also in theoretical chemistry.

Author : Denis J. Evans
Publisher : ANU E Press
Page : 318 pages
File Size : 15,53 MB
Release : 2007-08-01
Category : Science
ISBN : 1921313234

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"There is a symbiotic relationship between theoretical nonequilibrium statistical mechanics on the one hand and the theory and practice of computer simulation on the other. Sometimes, the initiative for progress has been with the pragmatic requirements of computer simulation and at other times, the initiative has been with the fundamental theory of nonequilibrium processes. This book summarises progress in this field up to 1990"--Publisher's description.

Author : Ilya Prigogine
Publisher : Courier Dover Publications
Page : 337 pages
File Size : 37,33 MB
Release : 2017-03-17
Category : Science
ISBN : 0486815552

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Groundbreaking monograph by Nobel Prize winner for researchers and graduate students covers Liouville equation, anharmonic solids, Brownian motion, weakly coupled gases, scattering theory and short-range forces, general kinetic equations, more. 1962 edition.

Author : Angelo Vulpiani
Publisher : World Scientific
Page : 482 pages
File Size : 44,20 MB
Release : 2010
Category : Mathematics
ISBN : 9814277665

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Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.

Author : Radu Balescu
Publisher : World Scientific
Page : 340 pages
File Size : 50,22 MB
Release : 1997-04-19
Category : Science
ISBN : 1783262613

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In the first part of this book, classical nonequilibrium statistical mechanics is developed. Starting from the Hamiltonian dynamics of the molecules, it leads through the irreversible kinetic equations to the level of fluid mechanics. For simple systems, all the transport coefficients are determined by the molecular properties.The second part of the book treats complex systems that require a more extensive use of statistical concepts. Such problems, which are at the forefront of research, include: continuous time random walks, non-Markovian diffusion processes, percolation and related critical phenomena, transport on fractal structures, transport and deterministic chaos. These “strange transport processes” differ significantly from the usual (diffusive) transport. Their inclusion in a general treatise on statistical mechanics is a special feature of this invaluable book./a