Stochastic transitions and statistical features of one-dimensional chains

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Abstract
Statistical consequences of the subdivision of the phase space of a classical nonlinear system (a Lennard-Jones chain) into regions of ordered and stochastic motions are investigated by numerical computations on two parameters, which are related to the average fluctuations and to the equipartition of the kinetic energy. While the former parameter behaves as if it were an ergodic function (i.e., its time average is correctly given by its canonical average), the time average of the latter cannot be so computed, and furthermore it exhibits a transition consistent with previous computations. Comparisons are made with a harmonic chain and with a Toda chain.