Does superfluid have substructure? I mean does the substructure matter?

My main research interest is the gravitational wave. Recently, I and my academic brother watched a famous video about the superfluid. I read a review then came up with some questions.

Here is the review: A. Schmitt, Introduction to Superfluidity —
Field-theoretical Approach and Applications, Lect. Notes Phys. 888 (2015) pp.1-155, arXiv:1404.1284.

Specifically, if one looks at section 3.3 (3.25) and (3.29) where the scalar field is written in form $$phi(X) = frac{rho(X)}{sqrt2}e^{ipsi(X)}.$$

Notice (3.25) $$n = rho^2cdotsigma tag{1},$$ and $$sigma ^2=partial_{mu}psi,partial^{mu}psi tag{2}$$
$sigma$ can be uniquely determined by (3.29) $P+varepsilon = sigmacdot n$ where $P$ is the pressure, $n$ is the charge density (in this case the number of helium), and $varepsilon$ is the energy density. Hence, by (1) and (2), one can determine the field function uniquely.

Therefore, can I state that if one fixes $n, P, text{and } varepsilon$, the field function is uniquely determined? Thus, the property of superfluid has nothing to do with the substructure (what forms the superfluid), or if one prefers, the information of substructure loses.