Made available in DSpace on 2015-03-03T15:16:25Z (GMT). No. of bitstreams: 1 AlysonPS_TESE.pdf: 964551 bytes, checksum: c9d496a0da4f410a6e8efa100d961e64 (MD5) Previous issue date: 2012-03-16 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / 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] / Considerando um g?s qu?ntico, os fundamentos da termoestat?stica padr?o s?o investigados no contexto da mec?nica estat?stica n?o-gaussiana introduzida por Tsallis e Kaniadakis. O novo formalismo ? baseado nas seguintes generaliza??es: i) entropia de Maxwell-Boltzmann-Gibbs e ii) dedu??o do Teorema-H. Com base neste estudo, calculamos uma nova entropia usando a generaliza??o da an?lise combinat?ria baseadas em dois diferentes m?todos de contagem. Os ingredientes b?sicos usados no teorema-H foram: uma entropia qu?ntica generalizada e uma generaliza??o do termo colisional da equa??o de Boltzmann. As distribui??es lei de pot?ncia calculadas s?o parametrizadas pelos par?metros q; , medindo o grau de n?o-gaussianidade do sistema. No limite q ?1; ?0, a termoestat?stica gaussiana ? recuperada. Um estudo complementar est? relacionado com um g?s perfeito no contexto da relatividade geral. Utilizando os efeitos n?o-gaussiano no conceito de fluxo de entropia, e no termo colisional da equa??o de transporte de Boltzmann, n?s generalizamos o teorema- H nos formalismos de Tsallis e Kaniadakis. No formalismo de Tsallis, o par?metro n?o extensivo est? restrito ao intervalo [0,2]

Made available in DSpace on 2015-03-03T15:15:26Z (GMT). No. of bitstreams: 1 EliangelaPB_DISSERT.pdf: 614353 bytes, checksum: 050737d0ef158e6082d81254619adac0 (MD5) Previous issue date: 2011-09-19 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / Considering a non-relativistic ideal gas, the standard foundations of kinetic theory are investigated in the context of non-gaussian statistical mechanics introduced by Kaniadakis. The new formalism is based on the generalization of the Boltzmann H-theorem and the deduction of Maxwells statistical distribution. The calculated power law distribution is parameterized through a parameter measuring the degree of non-gaussianity. In the limit = 0, the theory of gaussian Maxwell-Boltzmann distribution is recovered. Two physical applications of the non-gaussian effects have been considered. The first one, the -Doppler broadening of spectral lines from an excited gas is obtained from analytical expressions. The second one, a mathematical relationship between the entropic index and the stellar polytropic index is shown by using the thermodynamic formulation for self-gravitational systems / Considerando um g?s ideal n?o relativ?stico, os fundamentos da teoria cin?tica padr?o s?o investigados no contexto da mec?nica estat?stica n?o-gaussiana introduzida por Kaniadakis. O novo formalismo ? baseado na generaliza??o do teorema-H de Boltzmann e na dedu??o de Maxwell da distribui??o estat?stica. A distribui??o lei de pot?ncia calculada ? parametrizada por um par?metro medindo o grau de n?o-gaussianidade do sistema. No limite = 0, a teoria gaussiana de Maxwell-Boltzmann ? recuperada. Duas aplica??es dos efeitos n?o-gaussiano s?o estudados. Na primeira, o -alargamento Doppler das linhas espectrais de um g?s excitado ? obtido a partir das express?es anal?ticas. Na segunda, uma rela??o matem?tica entre o ?ndice entr?pico e o ?ndice politr?pico estelar ? mostrada usando uma formula??o termodin?mica para sistemas autogravitantes