Navier-Stokes equations for generalized thermostatistics

Abstract

Tsallis has proposed a generalization of Boltzmann-Gibbs thermostatistics by i n troducing a family of generalized nonextensive e n tropy functionals with a single parameter q. These reduce to the extensive Boltzmann-Gibbs form for q = 1, but a remarkable number of statistical and thermodynamic properties have been shown to be q-invariant that is, valid for any q. In this paper, we address the question of whether or not the value of q for a given viscous, incompressible uid can be ascertained solely by measurement of the uid's hydrodynamic properties. We nd that the hydrodynamic equations expressing conservation of mass and momentum are q-invariant, but the conservation of energy is not. Moreover, we nd that ratios of transport coe cients may also be q-dependent. These dependences may therefore be exploited to measure q experimentally.

Nonextensive models for earthquakes

“…Finally, it is worth mentioning that the estimates for the nonextensive parameter from the two catalogs here considered ( Fig. 1) are consistent with the upper limit q < 2, obtained from several independent studies involving the Tsallis nonextensive framework [20].…”

Transport coefficients and nonextensive statistics

“…We first notice that our main results are quite different from that ones obtained by Boghosian [7]. Probably, the basic reason comes from the fact that in his paper it was advocated a different choice to the BGK operator, namely,…”

Transport theory in the context of the normalized generalized statistics

“…In 1999, Boghosian [8] has obtained the hydrodynamic equations for the generalized statistics. He calculated them using the unnormalized q-expectation value and the well known Chapman-Enskog expansion.…”