The use of superfluid helium as a refrigerant in cryogenic systems is governed by the presence of a chaotic tangle of quantum filaments in the superfluid component of helium. Therefore, to describe any hydrodynamic phenomena (in particular, heat transfer) in quantumliquids containing vortex tangles, it is necessary to have information on their structure and statistics. The paper discusses two possible statistical configurations of chaotic vortices: the thermodynamic equilibrium and the highly nonequilibrium turbulent state, as well as the transition between them. Basing on the Langevin approach, we discuss the mechanism of establishment of thermodynamic equilibrium for a chaotic set of quantum vortex filaments. The corresponding Fokker–Planck equation for the probability density functional has a solution in the form of the Gibbs distribution. Basing on the above analysis, we discuss the possible causes and mechanisms of violation of thermodynamic equilibrium and transition to the turbulent regime.