Formação de caudas maxwellianas no Contexto da rotação estelar

In this Thesis, we analyzed the formation of maxwellian tails of the distributions of the rotational velocity in the context of the out of equilibrium Boltzmann Gibbs statistical mechanics. We start from a unified model for the angular momentum loss rate which made possible the construction of a general theory for the rotational decay in the which, finally, through the compilation between standard Maxwellian and the relation of rotational decay, we defined the (_, _) Maxwellian distributions. The results reveal that the out of equilibrium Boltzmann Gibbs statistics supplies us results as good as the one of the Tsallis and Kaniadakis generalized statistics, besides allowing fittings controlled by physical properties extracted of the own theory of stellar rotation. In addition, our results point out that these generalized statistics converge to the one of Boltzmann Gibbs when we inserted, in your respective functions of distributions, a rotational velocity defined as a distribution

Processos difusivos generalizados

We investigate several diffusion equations which extend the usual one by considering the presence of nonlinear terms or a memory effect on the diffusive term. We also considered a spatial time dependent diffusion coefficient. For these equations we have obtained a new classes of solutions and studied the connection of them with the anomalous diffusion process. We start by considering a nonlinear diffusion equation with a spatial time dependent diffusion coefficient. The solutions obtained for this case generalize the usual one and can be expressed in terms of the q-exponential and q-logarithm functions present in the generalized thermostatistics context (Tsallis formalism). After, a nonlinear external force is considered. For this case the solutions can be also expressed in terms of the q-exponential and q-logarithm functions. However, by a suitable choice of the nonlinear external force, we may have an exponential behavior, suggesting a connection with standard thermostatistics. This fact reveals that these solutions may present an anomalous relaxation process and then, reach an equilibrium state of the kind Boltzmann- Gibbs. Next, we investigate a nonmarkovian linear diffusion equation that presents a kernel leading to the anomalous diffusive process. Particularly, our first choice leads to both a the usual behavior and anomalous behavior obtained through a fractionalderivative equation. The results obtained, within this context, correspond to a change in the waiting-time distribution for jumps in the formalism of random walks. These modifications had direct influence in the solutions, that turned out to be expressed in terms of the Mittag-Leffler or H of Fox functions. In this way, the second moment associated to these distributions led to an anomalous spread of the distribution, in contrast to the usual situation where one finds a linear increase with time

Termoestatística quântica: uma abordagem via estatísticas não-gaussianas

Considering a quantum gas, the foundations of standard thermostatistics are investigated in the context of non-Gaussian statistical mechanics introduced by Tsallis and Kaniadakis. The new formalism is based on the following generalizations: i) Maxwell- Boltzmann-Gibbs entropy and ii) deduction of H-theorem. Based on this investigation, we calculate a new entropy using a generalization of combinatorial analysis based on two different methods of counting. The basic ingredients used in the H-theorem were: a generalized quantum entropy and a generalization of collisional term of Boltzmann equation. The power law distributions are parameterized by parameters q;, measuring the degree of non-Gaussianity of quantum gas. In the limit q