Thermodynamics of random walking vortex loops in counterflowing superfluids

Based on the theory of the thermodynamic equilibrium in a system of quantum vortices in superfluids in the presence of a counterflow, the influence of a vortex tangle on various thermodynamic phenomena in quantum liquids is studied. Using the early calculated partition function we study some of the properties of He II related to counterflow, such as the distribution of vortex loops in their length, the suppression of the superfluid density $\rho _{s}$ and the shift $T_{\lambda}$. Good agreement with the early obtained results is a fairly strong argument in favor of the point of view that the gas of string-like topological excitations can indeed be considered as a additional kind of quasi-particles having the inner structure at high temperatures, especially near the phase transition. The application of the developed formalism to the theory of quantum turbulence is briefly discussed.