Context Of Nonextensive Statistics Research Articles

Emerging extreme value and Fermi-Dirac distributions in the Lévy branching and annihilating process.

We study the dynamics of the branching and annihilating process with long-range interactions. Static particles generate an offspring and annihilate upon contact. The branching distance is supposed to follow a Lévy-like power-law distribution with P(r)∝1/r^{α}. We analyze the long term behavior of the mean particles number and its fluctuations as a function of the parameter α that controls the range of the branching process. We show that the dynamic exponent associated with the particle number fluctuations varies continuously for α<4 while the particle number exponent only changes for α<3. A crossover from extreme value Frechet (at α=3) and Gumbell (for 2<α<3) distributions is developed, similar to the one reported in recent experiments with cw-pumped random fiber lasers presenting underlying gain and Lévy processes. We report the dependence of the relevant dynamical power-law exponents on α showing that explosive growth takes place for α≤2. Further, the average occupation number distribution is shown to evolve from the standard Fermi-Dirac form to the generalized one within the context of nonextensive statistics.

Cosmology in a non-standard statistical background

We study the primordial neutron to baryon ratio in a cosmological expanding background within the context of non-extensive statistics, in a fully analytical approach. First order corrections to the weak interaction rates and energy densities in the early universe are obtained and their consequences on the Helium synthesis are analyzed. We find that, if the nucleosynthesis scenario should be in agreement with observation, this entails a very restrictive bound upon q, the non-extensive parameter. We also study some cosmologically interesting situations such as the moment of pair annihilation, conserved comoving quantities and derive for the nonextensive statistics, temperature relationships, before and after the removal of pairs.