An Introduction to Chaos in Nonequilibrium Statistical Mechanics

by J. R. Dorfman

Overview

This book provides an introduction to nonequilibrium statistical mechanics applied to ideas in chaotic dynamics. The author illustrates how techniques in statistical mechanics can be used to calculate quantities that are essential to understanding the chaotic behavior of fluid systems. Beginning with important background information, the volume goes on to introduce basic concepts of dynamical systems theory through simple examples before explaining advanced topics such as SRB and Gibbs measures. It will be of great interest to graduate students and researchers in condensed matter physics, nonlinear science, theoretical physics, mathematics, and theoretical chemistry.

Product Details

ISBN-13:	9780521655897
Publisher:	Cambridge University Press
Publication date:	08/28/1999
Series:	Cambridge Lecture Notes in Physics , #14
Edition description:	New Edition
Pages:	304
Product dimensions:	6.02(w) x 9.02(h) x 0.67(d)

Table of Contents

Preface; 1. Non-equilibrium statistical mechanics; 2. The Boltzmann equation; 3. Liouville's equation; 4. Poincaré recurrence theorem; 5. Boltzmann's ergodic hypothesis; 6. Gibbs' picture-mixing systems; 7. The Green-Kubo formulae; 8. The Baker's transformation; 9. Lyapunov exponents for a map; 10. The Baker's transformation is ergodic; 11. Kolmogorov-Sinai entropy; 12. The Frobenius-Perron equation; 13. Open systems and escape-rates; 14. Transport coefficients and chaos; 15. SRB and Gibbs measures; 16. Fractal forms in Green-Kubo relations; 17. Unstable periodic orbits; 18. Lorentz lattice gases; 19. Dynamical foundations of the Boltzmann equation; 20. The Boltzmann equation returns; 21. What's next; Appendices; Bibliography.

Editorial Reviews

"...a very valuable, enjoyable, and useful book to be highly recommended to any student or professional in the field of statistical mechanics at large." SIAM

"The entire book makes enjoyable and informative reading and is warmly recommended to anybody interested in either nonequilibrium statistical mechanics or dynamical systems theory, or both...Thirty-odd years of the author's expertise together with his clarity style make this set of lectures a real treat." Pageoph

"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." Mathematical Reviews

"...a first and needed step toward a systematic simple presentation of a developing methodology." Physics Today

"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 feild. 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." Jrnl of Statistical Physics Vol.104,

From the Publisher