Kolmogorov-Sinai entropy for dilute systems of hard particles in equilibrium.
In an equilibrium system, the Kolmogorov-Sinai entropy h(KS) equals the sum of the positive Lyapunov exponents, the exponential rates of divergence of infinitesimal perturbations. Kinetic theory may be used to calculate the Kolmogorov-Sinai entropy for dilute gases of many hard disks or spheres in equilibrium at low number density n. The density expansion of h(KS) is NnuA[ln n + B + O(n)], where nu is the single-particle collision frequency. Previous calculations of A were successful. Calculations of B , however, were unsatisfactory. In this paper, I show how the probability distribution of the stretching factor can be determined from a nonlinear differential equation by an iterative method. From this the Kolmogorov-Sinai entropy follows as the average of the logarithm of the stretching factor per unit time. I calculate approximate values of B and compare these to results from existing simulations. The agreement is good.
de Wijn
Astrid S
AS
Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE, Utrecht, The Netherlands. A.S.de.Wijn@phys.uu.nl