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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]
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/18622 |
| Date | 16 March 2012 |
| Creators | Santos, Alyson Paulo |
| Contributors | CPF:72106310463, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4790590E2, Silva, Luciano Rodrigues da, CPF:07416407400, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4783310Y1, Anselmo, Dory H?lio Aires de Lima, CPF:59764708404, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4790590Y7, Lenzi, Ervin Kaminski, CPF:01730626955, http://lattes.cnpq.br/9644741302334554, Silva J?nior, Raimundo |
| Publisher | Universidade Federal do Rio Grande do Norte, Programa de P?s-Gradua??o em F?sica, UFRN, BR, F?sica da Mat?ria Condensada; Astrof?sica e Cosmologia; F?sica da Ionosfera |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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