Navier-Stokes Equations for Generalized Thermostatistics

Tsallis has proposed a generalization of Boltzmann-Gibbs thermostatistics by introducing a family of generalized nonextensive entropy 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 fluid can be ascertained solely by measurement of the fluid's hydrodynamic properties. We find that the hydrodynamic equations expressing conservation of mass and momentum are $q$-invariant, but that for conservation of energy is not. Moreover, we find that ratios of transport coefficients may also be $q$-dependent. These dependences may therefore be exploited to measure $q$ experimentally.Comment: RevTeX and epsf macros required, 19 pages, 8 figure

A Particulate Basis for an Immiscible Lattice-Gas Model

We show that a phenomenological hydrodynamic lattice-gas model of two-phase flow, developed by Rothman and Keller in 1988 and used extensively for numerical simulations since then, can be derived from an underlying model of particle interactions. From this result, we elucidate the nature of the hydrodynamic limit of the Rothman-Keller model.Comment: 11 pages. Accepted for publication in Computer Physics Communication

From Dirac to Diffusion: Decoherence in Quantum Lattice Gases

We describe a model for the interaction of the internal (spin) degree of freedom of a quantum lattice-gas particle with an environmental bath. We impose the constraints that the particle-bath interaction be fixed, while the state of the bath is random, and that the effect of the particle-bath interaction be parity invariant. The condition of parity invariance defines a subgroup of the unitary group of actions on the spin degree of freedom and the bath. We derive a general constraint on the Lie algebra of the unitary group which defines this subgroup, and hence guarantees parity invariance of the particle-bath interaction. We show that generalizing the quantum lattice gas in this way produces a model having both classical and quantum discrete random walks as different limits. We present preliminary simulation results illustrating the intermediate behavior in the presence of weak quantum noise.Comment: To appear in QI