Time scales of relaxation and Lyapunov instabilities in a one-dimensional gravitating sheet system

Abstract

The relation between relaxation, the time scale of Lyapunov instabilities, and the Kolmogorov-Sinai time in a one-dimensional gravitating sheet system is studied. Both the maximum Lyapunov exponent and the Kolmogorov-Sinai entropy decrease as proportional to $N^{-1/5}$. The time scales determined by these quantities evidently differ from any type of relaxation time found in the previous investigations. The relaxation time to quasiequilibria (microscopic relaxation) is found to coincide with the inverse of the minimum positive Lyapunov exponent. The relaxation time to the final thermal equilibrium differs to the inverse of the Lyapunov exponents and the Kolmogorov-Sinai time.