A chain rule and a subadditivity for the entropy of type β, which is one of the nonextensive (nonadditive) entropies, were derived by Z.Daróczy. In this paper, we study the further relations among Tsallis type entropies which are typical nonextensive entropies. We show some inequalities related to Tsallis entropies, especially the strong subadditivity for Tsallis type entropies and the subaddit...

The nonextensive entropy of Tsallis can be seen as a consequence of postulates on a self-information, i.e., the constant ratio of the first derivative of a self-information per unit probability to the curvature (second variation) of it. This constancy holds if we regard the probability distribution as the gradient of a self-information. Considering the form of the nth derivative of a selfinform...

Using Rényi entropy, an alternative statistics to Tsallis one for nonextensive systems at equilibrium is discussed. We show that it is possible to have the q-exponential distribution function for equilibrium nonextensive systems having nonadditive energy but additive entropy. PACS : 02.50.-r, 05.20.-y, 05.70.-a

Using Rényi entropy, an alternative statistics to Tsallis one for nonextensive systems at equilibrium is discussed. We show that it is possible to have the q-exponential distribution function for equilibrium nonextensive systems having nonadditive energy but additive entropy. PACS : 02.50.-r, 05.20.-y, 05.30.-d,05.70.-a

The statistical properties of fully developed hydrodynamic turbulence can be successfully described using methods from nonextensive statistical mechanics. The predicted probability densities and scaling exponents precisely coincide with what is measured in various turbulence experiments. As a dynamical basis for nonextensive behaviour we consider nonlinear Langevin equations with fluctuating fr...

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