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  3. An Introduction to Chaos in Nonequilibrium Statistical Mechanics
  • Cited by 323
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
1999
Online ISBN:
9780511628870
DOI:
https://doi.org/10.1017/CBO9780511628870
Subjects:
Physics and Astronomy, Theoretical Physics and Mathematical Physics, Statistical Physics, Nonlinear Science and Fluid Dynamics
Series:
Cambridge Lecture Notes in Physics (14)
Information

Book description

This book is an introduction to the applications in nonequilibrium statistical mechanics of chaotic dynamics, and also to the use of techniques in statistical mechanics important for an understanding of the chaotic behaviour of fluid systems. The fundamental concepts of dynamical systems theory are reviewed and simple examples are given. Advanced topics including SRB and Gibbs measures, unstable periodic orbit expansions, and applications to billiard-ball systems, are then explained. The text emphasises the connections between transport coefficients, needed to describe macroscopic properties of fluid flows, and quantities, such as Lyapunov exponents and Kolmogorov-Sinai entropies, which describe the microscopic, chaotic behaviour of the fluid. Later chapters consider the roles of the expanding and contracting manifolds of hyperbolic dynamical systems and the large number of particles in macroscopic systems. Exercises, detailed references and suggestions for further reading are included.

Reviews

‘This book is a convincing invitation to modern mathematical concepts and new techniques. It will prove useful and attractive to graduate students and teachers in this active field.’

Yves Elskens Source: Mathematical Reviews

‘I recommend it highly … this book successfully gives its audience a unique and accessible up-to-date exposition of the mathematical foundation of Boltzmann’s statistical mechanics based on the modern ergotic theory of chaotic dynamical systems. This book will be valuable to applied mathematicians and theoretical physicists alike.’

Hong Qian Source: Bulletin of Mathematical Biology

‘It gives a good introduction to modern research in transport theory which relates macroscopic properties of large systems to underlying microscopic dynamics. The book does not pretend to be mathematically rigorous but presents an extremely readable account of the conceptual foundations of nonequilibrium statistical mechanics. To summarize, this is a very well written and readable book by one of the experts in the field. Its emphasis on conceptual developments, illustrated by simple dynamical models provides interesting reading not just for specialists, but also for a more general physical audience seeking a better understanding of the current status of the conceptual foundations of nonequilibrium statistical mechanics.’

Rudi Podgornik Source: Journal of Statistical Physics

‘… presents an extremely readable account of the conceptual foundations of nonequilibrium statistical mechanics … a very well written and readable book by one of the experts in the field … interesting reading not just for specialists, but also for a more general physical audience seeking a better understanding of the current status of the conceptual foundations of nonequilibrium statistical mechanics.’

Rudi Podgornik Source: Journal of Statistical Physics

‘The book presents a beautiful and detailed introduction to the major ideas behind modern developments in (classical) nonequilibrium statistical mechanics. … a very valuable, enjoyable, and useful book to be highly recommended to any student or professional in the field of statistical mechanics at large.’

Source: SIAM Review

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