The Kolmogorov -Sinai entropy for dilute gases in equilibrium

Abstract

We consider the density expansion of the Kolmogorov-Sinai (KS) entropy per particle for a dilute gas in equilibrium, and use methods from the kinetic theory of gases to compute the leading term. For an equilibrium system, the KS entropy hKS is the sum of all of the positive Lyapunov exponents characterizing the chaotic behavior of the gas. We compute hKS/N, where N is the number of particles in the gas. This quantity has a density expansion of the form hKS/N=aν[−lnñ+b+O(ñ)], where ν is the single-particle collision frequency and ñ 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.