Mean-Field Theory for Lyapunov Exponents and Kolmogorov-Sinai Entropy in Lorentz Lattice Gases

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Abstract
Chaotic properties of a Lorentz lattice gas are studied analytically and by computer simulations. The escape rates, Lyapunov exponents, and Kolmogorov-Sinai entropies are estimated for a 1D example using mean-field theory, and the results are compared with simulations for a range of densities and scattering parameters of the lattice gas. Computer results show a distribution of values for the dynamical quantities with average values in good agreement with mean-field theory, and consistent with the escape-rate formalism for the coefficient of diffusion.