Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system

We study the dynamics of a Hamiltonian system of N classical spins with infinite-range 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 thermodynamic 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.