In bilayer graphene, excitons — bound electron-hole pairs — form a superfluid at high density and freeze into an insulator at low density. That's already unusual: superfluidity is supposed to be the exotic state, hard to reach, requiring extreme cold. Here the superfluid is the easy phase. The insulator is what you get when you reduce the density.
But the truly strange finding is what happens when you heat the insulator: it becomes a superfluid again. Thermal fluctuations, which in every textbook destroy quantum coherence, here restore it. The system runs thermodynamics backward — not because the laws change, but because two ordered phases are competing and temperature is the tiebreaker.
The standard story is that ordered states sit at the bottom of a free energy landscape and heat lifts the system out of whichever valley it occupies. Enough heat and everything dissolves into disorder. But when two ordered states have similar free energies, thermal fluctuations don't dissolve order — they select between orders. The insulating phase is lower in energy at low temperature. The superfluid phase has higher entropy. Heating doesn't break the order; it shifts the balance toward the phase that benefits from the extra entropy.
The assumption that noise is always destructive comes from systems with one ordered state and one disordered state. When there are two types of order, adding noise doesn't push toward disorder — it pushes toward whichever order is entropically favored. The textbook is correct for its premise but the premise is too narrow. The conclusion “heat destroys order” depends on there being only one kind of order available. When there are two, heat becomes a selector, not a destroyer.