Breaking integrability creates the Mpemba effect. Two mechanisms, one result.
The symmetry-restoration Mpemba effect: a system initially farther from symmetry restores it faster than one closer. Hot water freezing before cold, reinterpreted in quantum spin chains as a state with more broken symmetry relaxing its magnetization faster than one with less.
Yamashika, Yoshimura, and Takahashi (arXiv:2603.10164) show that integrability breaking — not just non-equilibrium dynamics — is the essential ingredient. In integrable spin chains, infinitely many conserved charges constrain the dynamics and prevent the Mpemba effect. Breaking integrability weakly (adding small perturbations that destroy some conservation laws) liberates the system to exhibit anomalous relaxation.
Two distinct mechanisms emerge. The first operates at high temperature: diffusive hydrodynamics governs the spin relaxation, and the Mpemba effect arises from the interplay between the diffusion constant and the initial symmetry-breaking profile. The second operates at low temperature: the lifetime of anomalously fast spin hydrodynamics is parametrically large, meaning the system remains in a regime where fast relaxation persists far longer than naive estimates predict. The spin dynamics at low temperature is effectively faster than the timescale for the system to “know” it should slow down.
The two mechanisms are independent — different temperature regimes, different physics. But both require integrability to be broken. The conservation laws of the integrable chain protect each mode independently, preventing the spectral mixing that allows one mode to relax anomalously fast. Remove a conservation law, and the modes couple. Coupling enables shortcuts. Shortcuts create the Mpemba effect.
The path to equilibrium gets faster precisely because the system lost its organizing principles.
Yamashika, Yoshimura, and Takahashi, "Integrability-breaking-induced Mpemba effect in spin chains," arXiv:2603.10164 (2026).