Spelling suggestions: "subject:"estat?ética dde papadakis"" "subject:"estat?ética dee papadakis""
1 |
Termoestat?stica qu?ntica: uma abordagem via estat?sticas n?o-gaussianasSantos, Alyson Paulo 16 March 2012 (has links)
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]
|
Page generated in 0.3326 seconds