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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 q e ~ 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 thermodynamical sense. This generalization was first proposed in 1988… (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 Sq , 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)

- Constantino Tsallis, Andre M. C. Souza
- Physical review. E, Statistical, nonlinear, and…
- 2003

The basic aspects of both Boltzmann-Gibbs (BG) and nonextensive statistical mechanics can be seen through three different stages. First, the proposal of an entropic functional (S(BG)=-k Sigma(i)p(i)ln p(i) for the BG formalism) with the appropriate constraints (Sigma(i)p(i)=1 and Sigma(i)p(i)E(i)=U for the BG canonical ensemble). Second, through… (More)

- Domingo Prato, Constantino Tsallis
- Physical review. E, Statistical physics, plasmas…
- 1999

A deep connection between the ubiquity of Lévy distributions in nature and the nonextensive thermal statistics introduced a decade ago has been established recently [Tsallis et al., Phys. Rev. Lett. 75, 3589 (1995)], by using unnormalized q-expectation values. It has just been argued on physical grounds that normalized q-expectation values should be used… (More)

- Constantino Tsallis
- Entropy
- 2011

The nonadditive entropy Sq has been introduced in 1988 focusing on a generalization of Boltzmann–Gibbs (BG) statistical mechanics. The aim was to cover a (possibly wide) class of systems among those very many which violate hypothesis such as ergodicity, under which the BG theory is expected to be valid. It is now known that Sq has a large applicability;… (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)

- Fernando D. Nobre, Marco Aurélio Rego-Monteiro, Constantino 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 S1[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 Sq[p] = {1 − ∫ du [p(u)]q}/(q − 1)… (More)