Hot water can freeze faster than warm water. Erasto Mpemba observed this in 1963 while making ice cream in Tanzania. The effect resists clean explanation in classical thermodynamics — it depends on dissolved gases, evaporation, convection currents, container geometry. Sixty years later, the name migrated to quantum systems, where the mechanism is cleaner and the result is sharper.
Tilt a ferromagnet away from its symmetry axis. The spins point in a direction that breaks the system's rotational symmetry. Now quench the system — change the Hamiltonian suddenly and let the tilted state evolve. The symmetry gradually restores itself as the ferromagnetic order melts under quantum fluctuations. The quantum Mpemba effect: a state tilted further from the symmetric axis restores symmetry faster than a state tilted less.
The mechanism operates through entangled quasiparticle pairs generated by the quench. These pairs propagate ballistically with opposite momenta, carrying symmetry-breaking correlations out of any subsystem they exit. The key is velocity. States with larger initial symmetry breaking generate quasiparticle pairs whose symmetry-breaking content is concentrated in faster-moving modes. The correlations that encode the deviation are the ones most efficiently evacuated.
Measured through entanglement asymmetry — the difference between the Rényi entropy of a subsystem's state and its symmetrized version — the crossing is unambiguous. The more-broken state's asymmetry drops below the less-broken state's asymmetry at a definite time. The entanglement asymmetry vanishes if and only if the symmetry is fully restored, so this isn't a proxy. It's the thing itself.
The structural point is that the deviation produces the speed of its own correction. A larger tilt doesn't just mean more distance to travel — it means faster vehicles. The symmetry-breaking correlations generated by a larger perturbation are carried by quasiparticles that propagate more quickly, so the system that starts further from the target arrives first. The distance from equilibrium is not a debt to be repaid. It is the engine of repayment.