LYAPUNOV EXPONENTS AND KOLMOGOROV-SINAI ENTROPY FOR THE LORENTZ GAS AT LOW-DENSITIES

The Lyapunov exponents and the Kolmogorov-Sinai (KS) entropy for a two-dimensional Lorentz gas at low densities are defined for general nonequilibrium states and calculated with the use of a Lorentz-Boltzmann type equation. In equilibrium the density dependence of these quantities, predicted by Krylov, is recovered and explicit expressions are obtained. The relationship between KS entropy, Lyapunov exponents, and diffusion coefficients, developed by Gaspard and Nicolis, is generalized to a wide class of nonequilibrium states. © 1995 The American Physical Society.