An Introduction to Chaos in Nonequilibrium Statistical Mechanics

ISBN-13: 9780521655897 / Angielski / Miękka / 1999 / 304 str.

J. Robert Dorfman; Robert Dorfman; Peter Goddard

Opis

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.

Recenzje

'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

Spis treści

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.