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We give a closer look at the Central Limit Theorem (CLT) behavior inquasi-stationary states of the Hamiltonian Mean Field model, a paradigmatic onefor long-range-interacting classical many-body systems. We present newcalculations which show that, following their time evolution, we can observeand classify three kinds of long-standing quasi-stationary states (QSS) withdifferent correlations. The frequency of occurrence of each class depends onthe size of the system. The different microsocopic nature of the QSS leads todifferent dynamical correlations and therefore to different results for theobserved CLT behavior.

A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model