Termoestatística quântica: uma abordagem via estatísticas não-gaussianas - Santos, Alyson Paulo (2012)
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 1; 0, the gaussian thermostatistics is recovered. A complementary study is related to a perfect gas in the context of general relativity. Using the non-Gaussian effects on the concept of entropy flux, and on the collisional term of the Boltzmann equation, we generalize the H-theorem within the Tsallis and Kaniadakis frameworks. In the first one, the nonextensive parameter is constrained to the interval [0,2]