Hard Ball Systems and the Lorentz Gas
D. Szasz, L.A. Bunimovich, D. Burago, N. Chernov, E.G.D. Cohen, C.P. Dettmann, J.R. Dorfman, S. Ferleger, R. Hirschl, A. Kononenko, J.L. Lebowitz, C. Liverani, T.J. Murphy, J. Piasecki, H.A. Posch, N. Simanyi, Ya. Sinai, T. Tel, H. van Beijeren, R. van Zon, J. Vollmer, L.S. Young
Springer Science & Business Media, 11 dic. 2013 - 458 páginas
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.
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average billiard system Boltzmann equation boundary conditions Bunimovich cell central limit theorem Chernov clock values coarse-grained components constant convex correlation function corresponding curves cylindric billiard defined Dellago denote density deviation vectors dimensional dimensions disk dispersing billiards distribution dynamical systems entropy production equilibrium ergodic hypothesis ergodic theory exponential exponential decay field fluid gases geodesic geodesic flows Gibbs entropy Gibbs measure Hamiltonian hard ball systems hard spheres hyperbolic infinite initial conditions interaction invariant measure irreversible kinetic theory Kolmogorov-Sinai entropy KS entropy linear Lyapunov exponents macroscopic manifolds Markov partitions Math matrix motion multibaker map nonequilibrium number of collisions number of particles periodic Lorentz gas periodic orbits phase point phase space Phys physical Posch positive Lyapunov exponents potential proof proved scatterers semi-dispersing billiards sequence simulations Sinai singularity smooth statistical mechanics subspace symplectic tangent thermodynamic thermostat torus trajectory transport coefficients volume Wojtkowski zero