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Nonadditive entropy and nonextensive statistical mechanics - Some central concepts and recent applications
Constantino Tsallis, Ugur Tirnakli
We briefly review central concepts concerning nonextensive statistical mechanics, based on the nonadditive entropy $S_q=k\frac{1-\sum_{i}p_i^q}{q-1} (q \in {\cal R}; S_1=-k\sum_{i}…
Generalization of symmetric -stable Lévy distributions for
Sabir Umarov, Constantino Tsallis, Murray Gell-Mann +1
The -stable distributions introduced by Lévy play an important role in probabilistic theoretical studies and their various applications, e.g., in statistical physics, life scien…
Limit distributions of scale-invariant probabilistic models of correlated random variables with the q-Gaussian as an explicit example
Rudolf Hanel, Stefan Thurner, Constantino Tsallis
Extremization of the Boltzmann-Gibbs (BG) entropy under appropriate norm and width constraints yields the Gaussian distribution. Also, the basic solutions of the standard Fokker-Pl…
Comment on ``Proposed central limit behavior in deterministic dynamical systems''
Ugur Tirnakli, Constantino Tsallis, Christian Beck
In a recent Brief Report [Phys. Rev. E 79 (2009) 057201], Grassberger re-investigates probability densities of sums of iterates of the logistic map near the critical point and clai…
Nonextensivity at the edge of chaos of a new universality class of one-dimensional unimodal dissipative maps
Guiomar Ruiz, Constantino Tsallis
We introduce a new universality class of one-dimensional unimodal dissipative maps. The new family, from now on referred to as the ()-{\it logarithmic map}, corresponds to…