In a comparative study, the q-exponential and Weibull distributions are employed to investigate frequency distributions of basketball baskets, cyclone victims, brand-name drugs by retail sales, and highway length. In order to analyze the intermediate cases, a distribution, the q-Weibull one,...

The major factor that drives a protein toward collapse and folding is the hydrophobic effect. At the folding process a hydrophobic core is shielded by the solvent-accessible surface area of the protein. We study the fractal behavior of 5526 protein structures present in the Brookhaven Protein...

In this paper, we show a mathematical construction of Beck–Cohen superstatistics in the Bayesian point of view with the help of the two representations of a gamma function. Furthermore, it is shown how some results for superstatistics are related to each other.

We investigate the fluctuation of the energy in the framework of Tsallis statistics and find the correlation plays an important role in energy fluctuations. In Tsallis statistics, the correlation is induced by the nonextensivity of Tsallis entropy and exists between particles even if the...

Implications from a thermostatistics based on normalized Tsallis entropy, introduced by Rajagopal and Abe (Phys. Rev. Lett. 83 (1999) 1911) are analyzed. In particular, this normalization gives the thermodynamic stability, Cq0, for Tsallis formalism, leading to a natural extension to the...

Recently the Generalized Genetic Algorithm has been proposed, based on genetic algorithms and Tsallis statistics. Here, we study molecular preferences of the simple molecules and polypeptides by coupling the Generalized Genetic Algorithm and both a classical force field and a semi-empirical...

We prove a theorem stating that, within an interesting class of stationary solutions of the Liouville equation, the Tsallis q-distributions are the only ones that satisfy a condition which guarantees the existence of an integrating factor for the heat. The functional forms of the distribution as...

Oikonomou [Th. Oikonomou, Physica A 386 (2007) 119] has published a calculation which purports to show that the Tsallis and Rényi entropies can be obtained from the generalized multinomial coefficients. In this paper, we prove that the method of generalized multinomial coefficients failed to...

For a paradigmatic case, the standard map, we discuss how the statistical description of the approach to equilibrium is related to the sensitivity to the initial conditions of the system. Using a numerical analysis we present an anomalous scenario that may give some insight on the foundations of...

The universal character of the dynamics of various extreme phenomena is an outstanding scientific challenge. We show that X-ray flux and Dst time series during powerful solar flares and intense magnetic storms, respectively, obey a nonextensive energy distribution function for earthquake...