Closed chaotic quantum systems relax after a quench from a typical initial state into a Gibbs ensemble. At late times, the relaxation behavior is determined by their conservation laws and hydrodynamics. For specific initial states, this picture can break down. As a result, there exist pairs of initial states which asymptotically evolve to the same ensemble, yet exhibit drastically different relaxation. We show in two chaotic spin chains how this enables the quantum strong Mpemba effect: A system initially closer to equilibrium relaxes qualitatively slower than one that starts farther away, despite both approaching the same final state.

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• Anomalous diffusion
• Eigenstate thermalization
• Quantum quench
• Floquet systems
• Quantum spin models
• Statistical hydrodynamics