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-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

Fundamentação cinética da estatística não gaussiana : efeitos em politrópicas

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