14 - Transport in Nonequilibrium Steady States

Summary

Long time tails in Green-Kubo formulas for transport coefficients indicate that long range correlations in non-equilibrium fluids cause divergent transport coefficients in the Navier-Stokes equations for two dimensional fluids, and divergent higher order gradient corrections to these equations for three dimensional fluids. Possible resolutions of these difficulties are considered, for transport of momentum or energy in fluids maintained in non-equilibrium stationary states. The resolutions of the divergence difficulties depend on the particular flow under consideration. For stationary Couette flow in a gas, the divergences are resolved by including non-linear terms in the kinetic equations, leading to logarithmic terms in the velocity gradients for the equations of fluid flow for two dimensional gases, and fractional powers for three dimensional flows. Methods used for Couette flow do not resolve the divergence problems for stationary heat flow. Instead, the difficulties are resolved by taking the finite size of the system into account.