As additivity is a characteristic property of the classical information measure, Shannon entropy, pseudo-additivity of the form x+qy = x+y+(1−q)xy is a characteristic property of Tsallis entropy. Rényi in [1] generalized Shannon entropy by means of Kolmogorov-Nagumo averages, by imposing additivity as a constraint. In this paper we show that there exists no generalization for Tsallis entropy, b...

Usually, the Kohlrausch (stretched exponential) function is employed to fit the luminescence decays. In this work we propose to use the Tsallis distribution as an alternative to describe them. We show that the curves of the luminescence decay obtained from the Tsallis distribution are close to those ones obtained from the stretched exponential. Further, we show that our result can fit well the ...

Spin relaxation close to the glass temperature of CuMn and AuFe spin glasses is shown, by neutron spin echo, to follow a generalized exponential function which explicitly introduces hierarchically constrained dynamics and macroscopic interactions. The interaction parameter is directly related to the normalized Tsallis nonextensive entropy parameter q and exhibits universal scaling with reduced ...

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Rényi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingl...

It is shown that distributions arising in Rényi-Tsallis maximum entropy setting are related to the Generalized Pareto Distributions (GPD) that are widely used for modeling the tails of distributions. The relevance of such modelization, as well as the ubiquity of GPD in practical situations follows from Balkema-De Haan-Pickands theorem on the distribution of excesses (over a high threshold). We ...

Artificial neural networks are currently one of the most commonly used classifiers and over the recent years they have been successfully used in many practical applications, including banking and finance, health and medicine, engineering and manufacturing. A large number of error functions have been proposed in the literature to achieve a better predictive power. However, only a few works emplo...

Entropy is a key measure in studies related to information theory and its many applications. Campbell of the first time recognized that exponential of Shannon’s entropy is just the size of the sample space when the distribution is uniform. In this paper, we introduce a quantity which is called exponential Tsallis-Havrda-Charvat entropy and discuss its some properties. Further, we gave the appli...

in this article, the effect of the nonextensivity parameter on the energy fluctuations of nonextensive systems is studied in two different versions of the tsallis statistical mechanics. once a general expression has been reported for the energy fluctuations in the second version (tsallis work in 1988), the energy fluctuations of an ideal gas and a harmonic oscillator are studied in the second a...

In this paper we utilize the Tsallis relative entropy, a generalization of the Kullback–Leibler entropy in the frame work of non-extensive thermodynamics to analyze the properties of anomalous diffusion processes. Anomalous (super-) diffusive behavior can be described by fractional diffusion equations, where the second order space derivative is extended to fractional order α ∈ (1, 2). They repr...

The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This en-tropy is a variant of the generalized entropy of order α, considered in Mathai and Rathie (1975), and it is also associated with Shannon, Boltzmann-Gibbs, Rényi, Tsallis, and Havrda-Charvát entropies. The generalized entropy measure introduced here is also shown to...