Hard Ball Systems and the Lorentz Gas

Hard Ball Systems and the Lorentz Gas are fundamental models arising in the theory of Hamiltonian dynamical systems. Moreover, in these models, some key laws of statistical physics can also be tested or even established by mathematically rigorous tools. The mathematical methods are most beautiful but sometimes quite involved. This collection of surveys written by leading researchers of the fields - mathematicians, physicists or mathematical physicists - treat both mathematically rigourous results, and evolving physical theories where the methods are analytic or computational. Some basic topics: hyperbolicity and ergodicity, correlation decay, Lyapunov exponents, Kolmogorov-Sinai entropy, entropy production, irreversibility. This collection is a unique introduction into the subject for graduate students, postdocs or researchers - in both mathematics and physics - who want to start working in the field.

Outstanding research in dynamical systems. Includes supplementary material: sn.pub/extras

Zusammenfassung

"... The reviews have been written for a non-specialist mature audience and are quite accessible, even in the first part. The bibliography is very generous. Overall, the book constitutes an excellent introduction into this active, sometimes controversial, field. Anybody interested in the recent advances of dynamical systems theory applied to non-equilibrium statistical mechanics will find this book of use. ..."

Daniel Wójcik, Pure and Applied Geophysics 160, p. 1376-1378, 2003

Inhalt
Part I. Mathematics: D. Burago et al.: A Geometric Approach to Semi-Dispersing Billiards; T.J. Murphy et al.: On the Sequences of Collisions Among Hard Spheres in Infinite Space; N. Simányi: Hard Ball Systems and Semi-Dispersive Billiards: Hyperbolicity and Ergodicity; N. Chernov et al.: Decay of Correlations for Lorentz Gases and Hard Balls; N. Chernov: Entropy Values and Entropy Bounds; L.A. Bunimovich: Existence of Transport Coefficients; C. Liverani: Interacting Particles; J.L. Lebowitz et al.: Scaling Dynamics of a Massive Piston in an Ideal Gas.- Part II. Physics: H. van Beijeren et al.: Kinetic Theory Estimates for the Kolmogorov-Sinai Entropy, and the Largest Lyapunov Exponents for Dilute, Hard-Ball Gases and for Dilute, Random Lorentz Gases; H.A. Posch et al.: Simulation of Billiards and of Hard-Body Fluids; C.P. Dettmann: The Lorentz Gas: a Paradigm for Nonequilibrium Stationary States; T. Tél et al.: Entropy Balance, Multibaker Maps, and the Dynamics of the Lorentz Gas.- Appendix D. Szász: Boltzmann's Ergodic Hypothesis, a Conjecture for Centuries?