This book puts together non-equilibrium thermodynamics, heat transport properties of superfluid He II, and thermodynamic and dynamic aspects of quantum turbulence. A one-fluid extended model of superfluid helium, with heat flux as an additional independent variable, is presented and compared with the two-fluid model, to explore how both models complement each other. Important features arise in rotating situations and in superfluid turbulence, characterized by quantized vortices leading to ...