Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system

We study the dynamics of a Hamiltonian system of N classical spins with infiniterange interaction. We present numerical results which confirm the existence of metaequilibrium Quasi Stationary States (QSS), characterized by non-Gaussian velocity distributions, anomalous diffusion, Lévy walks and dynamical correlation in phase-space. We show that the Termodynamic Limit (TL) and the Infinite-Time Limit (ITL) do not commute. Moreover, if the TL is taken before the ITL the system does not relax to the Boltzmann-Gibbs equilibrium, but remains in this new equilibrium state where nonextensive thermodynamics seems to apply.