Mean Field Theory for Lyapunov Exponents and KS Entropy in Lorentz   Lattice Gases
  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. 
M.H. Ernst, J.R. Dorfman, R. Nix, and D. Jacobs (Inst. for Theor.   Physics, Univ.of Utrecht, The Netherlands)