Entropy geometric construction of a pure substance with normal, superfluid and supersolid phases

TL;DR

This paper uses thermodynamics and empirical data to geometrically analyze the fundamental relation of pure substances, revealing differences between normal, superfluid, and supersolid phases, with implications for ultracold gas superfluidity.

Contribution

It introduces a geometric construction of the fundamental thermodynamic relation for substances with superfluid and supersolid phases, highlighting distinct entropy curves and chemical potential behaviors.

Findings

Normal substances have obtuse entropy level curves.

Quantum substances exhibit acute entropy level curves.

Identification of a potential supersolid phase region.

Abstract

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.