Teoria cinética não extensiva: efeitos físicos em gases e plasmas
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-Boltzma...
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| Formato: | doctoralThesis |
| Idioma: | por |
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Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/jspui/handle/123456789/16589 |
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| Resumo: | 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 |
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