Kinetic Theory Estimates for the Kolmogorov-Sinai Entropy, and
the Largest Lyapunov Exponents for Dilute, Hard-Ball Gases and
for Dilute, Random Lorentz Gases
The kinetic theory of gases provides methods for calculating Lyapunov exponents
and other quantities, such as Kolmogorov-Sinai entropies, that characterize
the chaotic behavior of hard-ball gases. Here we illustrate the use of
these methods for calculating the Kolmogorov-Sinai entropy, and the largest
positive Lyapunov exponent, for dilute hard-ball gases in equilibrium. The
calculation of the largest Lyapunov exponent makes interesting connections
with the theory of propagation of hydrodynamic fronts. Calculations are also
presented for the Lyapunov spectrum of dilute, random Lorentz gases in two
and three dimensions, which are considerably simpler than the corresponding
calculations for hard-ball gases. The article concludes with a brief discussion
of some interesting open problems
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