The q-state Potts model with long-range interactions that decay as 1/r subjected to a uniform magnetic field on d-dimensional lattices is analyzed for different values of q in the nonextensive regime 0<a<d . We calculate the mean-field solution of the model for all q and performed, for some values of q, Monte Carlo simulations for the spontaneous magnetization in the one-dimensional case. We sh...

Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras’ theorem. And hence, this property is referred to as Pythagoras’ theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical ...

Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics (with a non-additive q-entropy) of an ensemble of fractal strings and branes of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of gen...

In image processing, one of the most efficient techniques for image segmentation is entropy-based thresholding. In this work it was applied a generalized entropy formalism that represents a recent development in statistical mechanics. We propose, for the first time, an image thresholding method using a nonextensive entropy regarding the presence of nonadditive information content in some image ...

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...

The probability distributions (PDFs) of the differences of any physical variable in the intermittent, turbulent interplanetary medium are scale dependent. Strong non-Gaussianity of solar wind fluctuations applies for short time-lag spacecraft observations, corresponding to small-scale spatial separations, whereas for large scales the differences turn into a Gaussian normal distribution. These c...

Pronounced core-halo patterns of dark matter and gas density profiles, observed in relaxed galaxies and clusters, were hitherto fitted by empirical power-laws. On the other hand, similar features are well known from astrophysical plasma environments, subject to long-range interactions, modeled in the context of nonextensive entropy generalization. We link nonextensive statistics to the problem ...