Nonextensive statistical mechanics, pioneered by Tsallis, has recently achieved a generalization of the Gutenberg-Richter law for earthquakes. This remarkable generalization is combined here with natural time analysis, which enables the distinction of two origins of self-similarity, i.e., the process' memory and the process' increments infinite variance. By using also detrended fluctuation anal...

Thresholding is an important task in image processing. It is a main tool in pattern recognition, image segmentation, edge detection and scene analysis. In this paper, we present a new thresholding technique based on two-dimensional Tsallis entropy. The two-dimensional Tsallis entropy was obtained from the twodimensional histogram which was determined by using the gray value of the pixels and th...

Edges of an image are considered a type of crucial information that can be extracted by applying detectors with different methodology. It is a main tool in pattern recognition, image segmentation, edge detection and scene analysis. In this paper, we present a new technique of edge detection based on twodimensional Tsallis entropy. The two-dimensional Tsallis entropy was obtained from the two-di...

In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation value of a physical quantity: one is the ordinary definition and the other is the normalized q-expectation value employing the escort distribution. Since both of them lead to the maximum-Tsallis-entropy distributions of a similar type, it is of crucial importance to determine which the correct p...

A variety of phenomena in nuclear and high energy physics seemingly do not satisfy the basic hypothesis for possible stationary states to be of the type covered by Boltzmann-Gibbs (BG) statistical mechanics. More specifically, the system appears to relax, along time, on macroscopic states which violate the ergodic assumption. Some of these phenomena appear to follow, instead, the prescriptions ...

We present a formulation of Statistical Mechanics based on the concept of the dimensionless characteristic thermodynamic function, which has the form of a negative Massieu-Planck generalized potential. This function is equivalent to the free energy of the system in kT units. We construct classes of configurations in terms of the constraints of the system and, by applying the condition of minimu...

The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are derived. Notions of additivity, extensivity and homogeneity are clarified. The relation between mean code lengths in coding theory and various expressions for ...

A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very natural way following the Feynman proof for the usual statistical mechanics. The inequality turns out to be form-invariant with respect to the entropic index ...

We review uses of Tsallis statistical mechanics in the protein folding problem. Monte Carlo simulated annealing algorithm and generalized-ensemble algorithm with both Monte Carlo and stochastic dynamics algorithms are discussed. Simulations by these algorithms are performed for a penta peptide, Met-enkephalin. In particular, for generalized-ensemble algorithms, it is shown that from only one si...

We show that if we require positive definite probabilities, then frequently cited results of Prato, of Lenzi and Hilhorst on the nonextensive equilibrium statistical mechanics of gases are valid only for a limited range of the Tsallis parameter, q. We determine the range of validity of the Hilhorst and the Lenzi formulae. We then use various integral representations of the Gamma function to der...