Water, a liquid we've known since childhood, behaves like a crowded subway car. The hydrogen and oxygen molecules don't just jostle about: as they absorb energy, they constantly switch from a tight packing to a looser one. Each such move requires extra energy, so water soaks up heat with barely a rise in temperature.

For a long time, the cause was sought in quantum thermodynamics, but computer simulations powered by machine learning revealed otherwise. Quantum tweaks merely shift the backdrop; the star of the show is entropy (a measure of disorder)—its sharp jump when the packings switch. The ideas of Max Planck and Richard Feynman helped shape the model, but the answer came not from the quantum world, but from the geometry of hydrogen bonds.