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Kolmogorov-Sinai entropy and Lyapunov spectra of a hard-sphere gas

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  • Dellago, Ch.
  • Posch, H.A.

Abstract

The mixing behavior of a hard-sphere gas has its origin in the exponential growth of small perturbations in phase space. This instability is characterized by the so-called Lyapunov exponents. In this work, we compute full spectra of Lyapunov exponents for the hard-sphere gas for a wide range of densities ϱ and particle numbers by using a recently developed algorithm. In the dilute-gas regime, the maximum Lyapunov exponent is found to obey the Krylov relation λ ∝ ϱ ln ϱ, a formula exactly derived for the low-density Lorentz gas by Dorfman and van Beijeren. We study the system-size dependence and the effect of the fluid-solid-phase transition on the spectra. In the second part of this work we describe and test a direct simulation Monte Carlo method (DSMC) for the computation of Lyapunov spectra and present results for dilute hard-sphere gases. Excellent agreement is obtained with the results of the deterministic simulations. This suggests that the Lyapunov instability of a hard sphere gas may be analyzed within the framework of kinetic theory.

Suggested Citation

  • Dellago, Ch. & Posch, H.A., 1997. "Kolmogorov-Sinai entropy and Lyapunov spectra of a hard-sphere gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(1), pages 68-83.
    • Handle: RePEc:eee:phsmap:v:240:y:1997:i:1:p:68-83
    DOI: 10.1016/S0378-4371(97)00131-3
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