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...

We calculate the phase space volume Ω occupied by a nonextensive system of N classical particles described by an equilibrium (or steady-state, or long-term stationary state of a nonequilibrium system) distribution function, which slightly deviates from MaxwellBoltzmann (MB) distribution in the high energy tail. We explicitly require that the number of accessible microstates does not change resp...

In this paper, the Green function theory of quantum many-particle systems recently presented is reworked within the framework of nonextensive statistical mechanics with a new normalized q-expectation values. This reformulation introduces a renormalization of temperature of the earlier theory and a self-consistency condition. The linear response theory is also presented, along with its two-parti...

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...

Recently it has been shown by the present author [H. Hasegawa, Phys. Rev. E (in press): arXiv:0904.2399] that the interpolation approximation (IA) to the generalized Bose-Einstein and Femi-Dirac distributions yields results in agreement with the exact ones within the O(q − 1) and in highand low-temperature limits, where (q−1) expresses the non-extensivity: the case of q = 1 corresponding to the...

Stimulated by the recent debate on the physical relevance and on the predictivity of q-Gaussian formalism, we present specific analytical expressions for the parameters characterizing non-Gaussian distributions, such as the nonextensive parameter q, expressions that we have proposed for different physical systems, an important example being plasmas in the stellar cores.

The nonextensive statistics formalism proposed by Tsallis has found many applications in systems with memory effects, long range spatial correlations, and in general whenever the phase space has fractal or multi-fractal structure. These features may appear naturally in turbulent or non-neutral plasmas. In fact, the equilibrium distribution functions which maximize the nonextensive entropy stron...