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The domain of validity of standard thermodynamics and Boltzmann-Gibbs statistical mechanics is discussed and then formally enlarged in order to hopefully cover a variety of anomalous systems. The generalization concerns nonextensive systems, where nonextensivity is understood in the thermody-namical sense. This generalization was first proposed in 1988(More)
The optimization of the usual entropy S 1 [p] = − du p(u) ln p(u) under appropriate constraints is closely related to the Gaussian form of the exact time-dependent solution of the Fokker-Planck equation describing an important class of normal diffusions. We show here that the optimization of the generalized entropic form S q [p] = {1 − du [p(u)] q }/(q − 1)(More)
We present a molecular dynamics test of the Central Limit Theorem (CLT) in a paradigmatic long-range-interacting many-body classical Hamiltonian system, the HMF model. We calculate sums of velocities at equidistant times along deterministic trajectories for different sizes and energy densities. We show that, when the system is in a chaotic regime(More)
The q-Gaussian distribution is known to be an attractor of certain correlated systems, and is the distribution which, under appropriate constraints, maximizes the entropy S q , the basis of nonextensive statistical mechanics. This theory is postulated as a natural extension of the standard (Boltzmann-Gibbs) statistical mechanics, and may explain the(More)
We study the dynamics of a system of N classical spins with infinite-range interaction. We show that, if the thermodynamic limit is taken before the infinite-time limit, the system does not relax to the Boltzmann-Gibbs equilibrium, but exhibits different equilibrium properties, characterized by stable non-Gaussian velocity distributions, Lévy walks, and(More)