Navier-Stokes equations for generalized thermostatistics

Tsallis has proposed a generalization of Boltzmann-Gibbs thermostatistics b y introducing a family of generalized nonextensive entropy functionals with a single parameter q. These reduce to the extensive Boltzmann-Gibbs form f or q = 1, but a remarkable number of statistical and thermodynamic properti es have been shown to be q-invariant - that is, valid for any q. In this pa per, we address the question of whether or not the value of q for a given v iscous, incompressible fluid can be ascertained solely by measurement of th e fluid's hydrodynamic properties. Mie find that the hydrodynamic equations expressing conservation of mass and momentum are q-invariant., but the con servation of energy is not. Moreover, we find that ratios of transport coef ficients may also be q-dependent. These dependences may therefore be exploi ted to measure q experimentally.