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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Kolmogorov-Sinai entropy for dilute systems of hard particles in equilibrium
1Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE, Utrecht, The Netherlands. A.S.de.Wijn@phys.uu.nl
Abstract:
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.
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