Energy and Temperature of Superfluid Turbulent Vortex Tangles

We consider three aspects of turbulent vortex tangles in superfluids. First, we outline some contributions tothe Vinen’s equation for the time evolution of the vortex line density, related to the presence of pinned vorticesincorporating the effects of the walls. Afterwards, we analyze some aspects of the energy balance of the vortextangle, related to frictional dissipation and to vortex formation and destruction. Finally, we explore the conceptof an effective temperature for the vortex tangle, related to the average energy of the vortex loops and to thediffusion coefficient of vortex lines. The combination of these ideas suggests some formal similarities withother kinds of driven nonequilibrium systems characterized by several different temperatures.