The Dissipative Terms in the Hydrodynamic Equations 13

The system of equations, 8-22 to 8-25, obtained above describes the motion of a superfluid in the absence of energy dissipation. In reality, the lack of equilibrium leads to the appearance in all the fluxes, of terms depending on the derivatives of the velocities and thermodynamic variables, with respect to the coordinates. It must be noted that under nonequilibrium conditions the usual definitions of thermodynamic quantities lose their meaning and must be made more precise. If as before we denote by ρ the mass per unit volume of liquid and by j its momentum, then the continuity equation retains its usual form (9-1) ρ + div   j = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429502897/20d72e0b-9d39-4175-acc6-a943547edf8a/content/eq278.tif"/>