ABSTRACT
In this section, we derive the Gibbs distribution for a classical-field superfluid and utilize it to establish general (independent of microscopic details) thermodynamic relations and fundamental physical properties implied by them. In fact, the relations that we obtain for the classical field apply to quantum fields as well. We will see it when generalizing the theory to the quantum case. The physical reason for universality is that the relations in question are derived for the long-wave limit. The fact that we are dealing with long-wave physics is also crucial for understanding that the so-called ultraviolet (UV) catastrophe (the UV divergence of the integral for N at any finite temperature) inherent to most classical-field models, including the one considered here, does not affect these universal results. The particular form of the UV regularization is relevant only to the explicit form of the equations of state, playing no role in this section.
