UTe₂'s phase diagram contains what appears to be a thermodynamic impossibility: a triple point where two phase boundaries intersect. Triple points between three distinct phases are permitted, but the geometry here implies two boundaries crossing, which violates Gibbs' phase rule for the system's degrees of freedom.
Kamat, Dans, Saha, Kokovin, Paglione, Schmalian, and Ramshaw resolve the paradox with ultrasound. They detect a previously hidden phase boundary, marked by an anomalous upward shift in sound velocity—a feature invisible to standard thermodynamic probes. The “impossible” triple point is actually tetracritical: four phases meet, not three.
At this tetracritical point, two distinct superconducting order parameters merge into a multicomponent state. The competition between them causes the re-entrant behavior that made the phase diagram look wrong. Their eventual phase-locking reduces superconducting fluctuations—the system becomes more ordered precisely where more order parameters are active.
The lesson has two layers. First: apparent thermodynamic impossibilities may be evidence of hidden phases, not measurement errors. The correct response to a forbidden triple point is not to dismiss it but to look for what you're missing. Second: increasing the number of competing orders can produce greater stability. Two order parameters that individually fluctuate can lock together into a rigid composite with less fluctuation than either alone.
What looks like a thermodynamic impossibility is actually evidence of a hidden degree of freedom. The paradox was information, not error.