paper

Mean Field Theory for Lyapunov Exponents and KS Entropy in Lorentz Lattice Gases

arXiv:chao-dyn/9412013 · doi:10.1103/PhysRevLett.74.4416

Abstract

Cellular automata lattice gases are useful systems for systematically exploring the connections between non-equilibrium statisitcal mechanics and dynamical systems theory. Here the chaotic properties of a Lorentz lattice gas are studied analytically and by computer simulations. The escape-rates, Lyapunov exponents, and KS entropies are estimated for a one-dimensional example using a mean-field theory, and the results are compared with simulations for a range of densities and scattering parameters of the lattice gas. The computer results show a distribution of values for the dynamical quantities with average values that are in good agreement with the mean field theory, and consistent with the escape-rate formalism for the coefficient of diffusion.

New version with updated and corrected table of data from computer simulations; 11 pages, one figure included in file

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