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 ${h}_{\mathrm{KS}}$ is the sum of all of the positive Lyapunov exponents characterizing the chaotic behavior of the gas. We compute ${h}_{\mathrm{KS}}/N,$ where $N$ is the number of particles in the gas. This quantity has a density expansion of the form ${h}_{\mathrm{KS}}/N=a\ensuremath{\nu}[\ensuremath{-}\mathrm{ln}\~n+b+O(\~n)],$ where $\ensuremath{\nu}$ is the single-particle collision frequency and $\~n$ 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.