Statistical mechanics and thermodynamics of turbulent quantum vortex tangles

In this paper we present some phenomenological ideas about the thermodynamics of quantized vortex loops arising in superfluid turbulence. The system of vortex loops may be seen as a dissipative structure, not existing on its own but only under the influence of an external heat flux. Starting from a simple definition of the temperature of the vortex tangle and from the relation between energy and vortex length, we obtain the entropy of the system, as well as the caloric and thermal equations of state, relating internal energy and pressure to temperature and volume. We discuss the connection between our macroscopic results and microscopic results on vortex length distribution function having a potential form.