In this paper we discuss the nonergodic behavior for a class of long-standingquasi-stationary states in a paradigmatic model of long-range interactingsystems, i.e. the HMF model. We show that ensemble averages and time averagesfor velocities probability density functions (pdfs) do not coincide and inparticular the latter exhibit a tendency to converge towards a q-Gaussianattractor instead of the usual Gaussian one predicted by the Central LimitTheorem, when ergodicity applies.
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