Transport theory in the context of the normalized generalized statistics

Abstract

In this work assuming valid the equipartition theorem and using the normalized q-expectation value, we obtain, until first order approximation, the hydrodynamics equation for the generalized statistics. This equations are different from those obtained in the context of the Boltzmann-Gibbs statistics. This difference is that now appears two transport coefficient that depend on the q-value. PACS number(s): 05.20.Jj, 05.20.Gg

On the dependence of the Navier–Stokes equations on the distribution of molecular velocities

“…This additional term was also found by Boghosian and by Potiguar and Costa [2,3] in the derivation of the Navier Stokes equations for Tsallis thermostatistics, and is the only additional term allowed by the Curie principle.…”

“…Boghosian found that the incompressible limit of the Navier-Stokes equations is independent of the parameter q characterizing the Tsallis distribution, whereas the energy equation in the compressible case contains an additional q-dependent contribution to the heat flux [2]. This result was confirmed in [3], and the additional term is the only further term allowed by the Curie principle [12].…”

Transport coefficients and nonextensive statistics

“…It is interesting to compare our results (and the overall approach) with independent analyzes and some previous expressions to nonextensive transport coefficients appearing in the literature [7,10]. We first notice that our main results are quite different from that ones obtained by Boghosian [7].…”

Transport equations in magnetized plasmas for non-Maxwellian distribution functions

“…32 Similar fluid equations have been found from other transport models within q-statistics. 25,51 The first order solution of Eq. (38) is determined following the standard procedure of Refs.…”