We provide a unifying axiomatics for Rényi’s entropy and non–extensive entropy of Tsallis. It is shown that the resulting entropy coincides with Csiszár’s measure of directed divergence known from communication theory.

Within the Tsallis thermodynamics framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be recovered. Moreover, we also generalize Einstein's formula for the probability of a fluctuation to occur by means of the maximum statistical entropy method. ...

The general mathematical formulation of the equilibrium statistical mechanics based on the generalized statistical entropy for the first and second thermodynamic potentials was given. The Tsallis and Boltzmann-Gibbs statistical entropies in the canonical and microcanonical ensembles were investigated as an example. It was shown that the statistical mechanics based on the Tsallis statistical ent...

The two-dimensional (2-D) maximum Tsallis entropy method often gets ideal segmentation results, because it not only takes advantage of the spatial neighbor information with using the 2-D histogram of the image, but also has some flexibility with a parameter. However, its time-consuming computation is often an obstacle in real time application systems. In this paper, a fast image thresholding me...

when two systems are under consideration. In classical information theory, one employs the Kullback – Leibler relative entropy for this purpose which also has its quantum version. These are also additive measures and the Tsallis counterparts of these have been put forward and employed in the quantum context as well [10, 11]. There is promise in future work using the Tsallis approach to problems...

It is demonstrated clearly that for the same classic generalized system the Tsallis power-laws with both the 1 > q and the 1 < q can be induced by the constraint of the constant harmonic mean for the so-called reciprocal energies r E and at the same time the Boltzmann distribution or the negative exponential probability distribution can be generated with the constraint of the constant arithmeti...

Shannon entropy [1] is one of fundamental quantities in classical information theory and uniquely determinded by the Shannon-Khinchin axiom or the Faddeev axiom. Oneparameter extensions for Shannon entropy have been studied by many researchers [2]. The Rényi entropy [3] and the Tsallis entropy [4] are famous. In the paper [5], the uniqueness theorem for the Tsallis entropy was proven. See also ...

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 ...

Escort distributions are a simple one parameter deformation of an original distribution p. In Tsallis extended thermostatistics, the escort-averages, defined with respect to an escort distribution, have revealed useful in order to obtain analytical results and variational equations, with in particular the equilibrium distributions obtained as maxima of Rényi-Tsallis entropy subject to constrain...