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Previous issue date: 2000-06-02 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The standard kinetic theory for a nonrelativistic diluted gas is
generalized in the spirit of the nonextensive statistic distribution
introduced by Tsallis. The new formalism depends on an arbitrary q
parameter measuring the degree of nonextensivity. In the limit q = 1, the
extensive Maxwell-Boltzmann theory is recovered.
Starting from a purely kinetic deduction of the velocity q-distribution
function, the Boltzmann H-teorem is generalized for including the
possibility of nonextensive out of equilibrium effects. Based on this
investigation, it is proved that Tsallis' distribution is the necessary
and sufficient condition defining a thermodynamic equilibrium state in the
nonextensive context. This result follows naturally from the generalized
transport equation and also from the extended H-theorem.
Two physical applications of the nonextensive effects have been
considered. Closed analytic expressions were obtained for the Doppler
broadening of spectral lines from an excited gas, as well as, for the
dispersion relations describing the eletrostatic oscillations in a diluted
electronic plasma. In the later case, a comparison with the experimental
results strongly suggests a Tsallis distribution with the q parameter
smaller than unity.
A complementary study is related to the thermodynamic behavior of a
relativistic imperfect simple fluid. Using nonequilibrium thermodynamics,
we show how the basic primary variables, namely: the energy momentum
tensor, the particle and entropy fluxes depend on the several dissipative
processes present in the fluid. The temperature variation law for this
moving imperfect fluid is also obtained, and the Eckart and
Landau-Lifshitz formulations are recovered as particular cases / A teoria cin?tica padr?o para um g?s dilu?do n?o relativ?stico, ? generalizada no esp?rito da distribui??o estat?stica n?o-extensiva introduzida por Tsallis. O novo formalismo depende de um par?metro arbitr?rio q medindo o grau de n?o extensividade do sistema. No limite q = 1, a teoria extensiva de Maxwell-Boltzmann ? recuperada.
Iniciando com uma dedu??o puramente cin?tica da q-distribui??o de velocidades, o teorema-H de Boltzmann ? generalizado para incluir a possibilidade de efeitos n?o extensivos fora de equil?brio. Com base nesse estudo, demonstramos que a q-distribui??o de Tsallis ? uma condi??o necess?ria e suficiente para o equil?brio termodin?mico no regime n?o extensivo. Um resultado que segue naturalmente da equa??o de transporte generalizada e do novo teorema.
Duas aplica??es dos efeitos n?o-extensivos s?o consideradas. Express?es anal?ticas s?o obtidas para o q-alargamento Doppler das linhas espectrais de um g?s excitado e tamb?m para as rela??es de dispers?o descrevendo as oscila??es eletrost?ticas num plasma eletr?nico dilu?do. No segundo caso, uma compara??o com os resultados experimentais sugere fortemente uma distribui??o de Tsallis com par?metro q < 1.
Um estudo complementar est? relacionado com a termodin?mica de um fluido imperfeito relativ?stico. Utilizando a termodin?mica fora de equil?brio, n?s calculamos como as vari?veis prim?rias b?sicas: o tensor de energia-momento, o fluxo de part?culas e o de entropia dependem dos mais variados processos dissipativos. A taxa de varia??o da temperatura do fluido em movimento ? obtida, e as formula??es de Eckart e Landau-Lifshitz s?o recuperadas como casos particulares
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/16589 |
| Date | 02 June 2000 |
| Creators | Silva Junior, Raimundo |
| Contributors | CPF:10659682415, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4787078Z7, Silva, Luciano Rodrigues da, CPF:07416407400, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4783310Y1, Santos, Janilo, CPF:01999044487, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4763288H3, Bezerra, Valdir Barbosa, CPF:10999205404, http://lattes.cnpq.br/1945428104771588, Mohan, Madras Viswanathan Gandhi, CPF:04295882755, http://lattes.cnpq.br/1995273890709490, Lima, Jos? Ademir Sales de |
| 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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