Slices along the x = 0 and z = 0 planes of the calculated local degeneracy T / T F during transport through the 1D channel, showing that the reservoirs (left L and right R) are in local equilibrium in the normal phase (red, T / T F > 0.167) over most of their volume and superfluid (blue, T / T F <= 0.167) at the contacts to the channel. The channel (green) is far from local equilibrium. Differences in the atom number N , energy U and entropy S between the reservoirs induce currents between them.