  Using the laws of thermodynamics together with empirical data, we present a
qualitative geometric construction of the fundamental relation of a pure
substance $S = S(E,N,V)$, with $S$ entropy, $E$ energy, $N$ number of particles
and $V$ volume. We analyze two very general type of substances, a "normal" and
a "quantum" one, the main difference between them being that the latter
presents superfluid phases. It is found that the constant entropy level curves
are completely different in both cases, in the normal substances being obtuse
while acute in quantum ones. A concomitant signature of the previous result is
that the chemical potential can be both positive and negative in quantum
substances, but only negative in normal ones. Our results suggest the existence
of a region in the quantum substances that may be identified as a supersolid
phase. We also make emphasis on the relevance of the present study within the
context of superfluidity in ultracold gases.
