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With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namely Sq==-k[1-Zwt pq]/(q-1), where qe~ characterizes the generalization and {Pi} are the probabilities associated with W (microscopic) configurations (WE N). The main properties associated with this entropy are established, particularly those… (More)

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)

- Constantino Tsallis, Dirk Jan Bukman
- 1996

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)

Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to the initial conditions , mixing and ergodicity in Gibbs Γ-space. What are the corresponding hypothesis for nonextensive… (More)

- A Pluchino, A Rapisarda, C Tsallis
- 2007

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)

- Yuzuru Sato, Constantino Tsallis
- I. J. Bifurcation and Chaos
- 2006

" Beauty is truth, truth beauty, " – that is all Ye know on earth, and all ye need to know. An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q − 1 (entropic nonextensivity) as a simple and efficient manner to provide, at least for some… (More)

- William Thistleton, John A. Marsh, Kenric Nelson, Constantino Tsallis
- IEEE Trans. Information Theory
- 2007

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)

- V Latora, A Rapisarda, C Tsallis
- Physical review. E, Statistical, nonlinear, and…
- 2001

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)