On the dependence of thermodynamic variables on the relative velocity vns in a superfluid counterflowing helium

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 ρs, and the shift Tλ. The physics behind this issue is related to the fact that the partition function describing the ensemble of chaotic vortex filaments depends on the relative velocity vns. The partition function, in turn, depends on relative velocity due to the Gibbs distribution with the specific velocity-dependent Hamiltonian. Good agreement with the earlier obtained results is a fairly strong argument in favor of the point of view that a collection of chaotic quantum vortices can, indeed, be considered as a kind of gas of quasiparticles at high temperatures, especially near a phase transition. The work is closely related to nonlinear physics, which studies chaotic processes, and is currently in the stage of active development, resulting in many meaningful and expressive results. The application of the developed formalism to the theory of quantum turbulence is briefly discussed.