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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)

- F D Nobre, M A Rego-Monteiro, C Tsallis
- Physical review letters
- 2011

Generalizations of the three main equations of quantum physics, namely, the Schrödinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index q, are considered in such a way that the standard linear equations are recovered in the limit q→1. Interestingly, these equations present a common,… (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)

- Constantino Tsallis
- Entropy
- 2011

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

Many natural and artificial systems whose range of interaction is long enough are known to exhibit (quasi)stationary states that defy the standard, Boltzmann–Gibbs statistical mechanical prescriptions. For handling such anomalous systems (or at least some classes of them), nonextensive statistical mechanics has been proposed based on the entropy Sq ≡ k (1−… (More)

" 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)