An Introduction to Chaos in Nonequilibrium Statistical Mechanics

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

J. R. Dorfman (Author)

9780521655897, Cambridge University Press

Paperback, published 28 August 1999

304 pages
22.9 x 15.3 x 1.7 cm, 0.505 kg

'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.' SIAM Review

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.

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.

Subject Areas: Statistical physics [PHS]