The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium

Details The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium

1997-06-18

arxiv.org/abs/chao-dyn/9706019v1

Nonlinear Sciences

Chaotic Dynamics

15 pages, 2 figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.56.5272

We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy per particle for a dilute gas in equilibrium. For an equilibrium system, the KS entropy, h_KS is the sum of all of the positive Lyapunov exponents characterizing the chaotic behavior of the gas. We compute h_KS/N, where N is the number of particles in the gas. This quantity has a density expansion of the form h_KS/N = a\nu[-\ln{\tilde{n}} + b + O(\tilde{n})], where \nu is the single-particle collision frequency and \tilde{n} is the reduced number density of the gas. The theoretical values for the coefficients a and b are compared with the results of computer simulations, with excellent agreement for a, and less than satisfactory agreement for b. Possible reasons for this difference in b are discussed.

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