Kinetic Theory Estimates for the Kolmogorov-Sinai Entropy and the Largest Lyapunov Exponents for Dilute, Hard-Ball Gases and for Dilute, Random Lorentz Gases

摘要

The kinetic theory of gases provides methods for calculating Lyapunovexponents and other quantities, such as Kolmogorov-Sinai entropies, thatcharacterize the chaotic behavior of hard-ball gases. Here we illustrate theuse of these methods for calculating the Kolmogorov-Sinai entropy, and thelargest positive Lyapunov exponent, for dilute hard-ball gases in equilibrium.The calculation of the largest Lyapunov exponent makes interesting connectionswith the theory of propagation of hydrodynamic fronts. Calculations are alsopresented for the Lyapunov spectrum of dilute, random Lorentz gases in two andthree dimensions, which are considerably simpler than the correspondingcalculations for hard-ball gases. The article concludes with a brief discussionof some interesting open problems.