Abstract
We show that time averages of physical observables agree with ensemble averages provided chaos is present and widespread in a model system of coupled rotators. Slow relaxation is present both at low and at high temperature, where chaos is weak and inefficient. A 1.5 dimensional Hamiltonian describes the high dimensional motion quite well and allows the introduction of a Chirikov overlap parameter. A Gibbsian calculation of this parameter predicts the high temperature threshold to the statistical regime. The onset of nonlinearity is instead the mechanism which leads to the statistical regime on the low temperature side. This result should prove of interest for understanding and controlling the relaxation to equilibrium of molecular dynamics simulations. Moreover it indicates that perhaps the ergodic hypothesis is a too strong requirement.
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