Lyapunov Exponents and KS Entropy for the Lorentz Gas at Low Densities

The Lyapunov exponents and the KS entropy for a two dimensional Lorentz gas at low densities are defined for general non-equilibrium 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 the KS entropy, Lyapunov exponents, and escape rate, conjectured by Gaspard and Nicolis for non-equilibrium systems is confirmed and generalized.