# Why are superfluids thermodynamically possible?

I was reading about superfluids and how they can flow without loss of any kinetic energy over time, specifically they can form vortices that rotate indefinitely. However I do not understand why this is possible as surely the outside of a vortex is moving faster so particles over there have a greater kinetic energy than those closer to the centre so why is there no transfer of kinetic energy over time (say from collisions between particles) until all the particles have the same kinetic energy and the vortex just dissipates away?

• The mechanism of energy loss to heat in classical fluids is viscosity. But since superfluids have zero viscosity, no losses. Hence perpetual internal flow of energy. – docscience Jan 8 '17 at 18:35

Superfluidity is essentially the quantum phenomenon. All particles in superfluid has the same bosonic wavefunction with well-defined amplitude and phase (coherent state). This prevents any scattering and allows non-viscous flow.

Superfluid has certain stiffness against external perturbation, i.e. there is an energy gap for elementary excitations and only perturbations larger than the gap can create them. All other perturbations only deform the phase of the superfluid collective wavefunction.

Speed of superfluid is the gradient of the phase of wavefunction. Vortices in superfluid are irrotational, i.e. speed vanishes as $\propto 1/r$. Their vorticity (curl of velocity) is zero, except the very center of the vortex (the latter is not strict).

The speed of particles moving around the vortex line decreases away from it, so its kinetic energy is finite, hence the thermodynamic stability, as you put it.