Thermodynamically equilibrium quantum vortices in superfluid liquids

The thermodynamic equilibrium is studied for a system of quantised vortices in superfluid liquids in the presence of a counterflow of the normal and superfluid components. The partition function is calculated, which takes into account various configurations of the vortex filaments, as well as the distribution of loops in length. The dependence of the density of vortex filaments on the applied counterflow velocity is discussed.