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 ...

Connections between Tsallis' formalisms employing the standard linear average energy and ones employing the normalized q-average energy Abstract Tsallis' thermostatistics with the standard linear average energy is revisited by employing S 2−q , which is the Tsallis entropy with q replaced by 2 − q. We explore the connections among the S 2−q approach and the other different versions of Tsal-lis ...

It is demonstrated clearly that for the same classical 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 arithme...

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...

This study makes use of the Tsallis entropy to predict the shear stress distribution. Given a definition of the Tsallis entropy, it is maximized by using the probability density function, which then is used to attain a novel shear stress equation. This is then employed for calculating the shear stress distribution in rectangular channels in different aspect ratios and finally, for viability, th...

We address this work to investigate symbolic sequences with long-range correlations by using computational simulation. We analyze sequences with two, three and four symbols that could be repeated l times, with the probability distribution p(l) ∝ 1/lμ. For these sequences, we verified that the usual entropy increases more slowly when the symbols are correlated and the Tsallis entropy exhibits, f...

Entropy is well known to be Schur concave on finite alphabets. Recently, the authors have strengthened the result by showing that for any pair of probability distributions P and Q with Q majorized by P , the entropy of Q is larger than the entropy of P by the amount of relative entropy D(P ||Q). This result applies to P and Q defined on countable alphabets. This paper shows the counterpart of t...

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. ...