We examine possible closed form solutions for the cumulative distribution function for systems where the probability density function can be adequately described by the generalized non-extensive statistics framework. Application to financial time series as a possible Value at Risk technique...

We investigate the general property of the energy fluctuation in the canonical ensemble and the ensemble equivalence in Tsallis statistics. By taking the generalized ideal gas and the generalized harmonic oscillators as examples, we show that, when the particle number N is large enough, the...

We use q-Gaussian trial wave function, based on Tsallis statistics, to study, variationally, the ground state and vortex state energies of Bose–Einstein condensation of dilute ultracold alkali atoms in anisotropic traps. This trial function works well when compared with the results available...

In this study, the nematic–isotropic phase transition is investigated for a sample in the shape of a slab of thickness d, using nonextensive formalism. The interaction potential is written as the sum of the direct interaction of a given nematic molecule with the substrate and of its incomplete...

We calculate the fluctuation of a system's energy in Tsallis statistics following the finite heat bath canonical ensemble approach. We obtain this fluctuation as the second derivative of the logarithm of the partition function plus an additional term. We also find an explicit expression for the...

We derive the statistical distributions, partition functions and thermodynamic formulas for a completely open system on the basis of Tsallis entropy. These results are derived for two types of constraints, using the method of maximum entropy.

We propose a stochastic approach to combine methods from computational physics and Tsallis statistics in order to analyze the potential energy hypersurface of the proteins. This approach enables us to study protein folding by the topology of the energy hypersurface close to the native...

It is a remarkable fact that the traditional teaching of thermodynamics, as reflected in the textbooks and including the long developments about ensembles and thermodynamic functions, is almost entirely about systems in equilibrium. The time variable does not enter. There is one exception,...

Within the generalized statistical mechanics introduced recently by Tsallis, the generalized form of the affinities (the quantities which drive a process in the theory of irreversible thermodynamics) was derived. The affinities were obtained by considering changes in the generalized entropy...

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.