Hot water sometimes freezes before cold: this is the Mpemba effect. In the quantum realm, a similar paradox appears: the more the equilibrium is disrupted, the faster it recovers. It's like fleeing from disorder (entropy) in reverse: the system rushes toward order, and a large initial imbalance only helps. But quantum particles obey strict conservation rules, such as the laws of the Standard Model. These rules shatter the system's state into isolated compartments, like an ice tray with dividers. It turns out that in this fragmented system, the Mpemba effect appears twice: one kind of imbalance 'melts' away quickly, another — more slowly. Some compartments are frozen forever: imbalance is preserved there, holding a memory of the initial state. These compartments are a quantum chronicle that can outlive the system itself. Active compartments race toward balance, giving rise to the paradox. The ideas of Ludwig Boltzmann on entropy and probability and John von Neumann on quantum disorder intertwine into a tapestry of memory and forgetting.
as written by the authors arXiv:2606.06653
A quantum system can restore a broken symmetry faster the more strongly it initially breaks it, an anomaly known as the quantum Mpemba effect. Whether this effect survives once conservation laws fragment the Hilbert space into exponentially many disconnected Krylov sectors has remained open. We address this question for circuits and Hamiltonians with simultaneous charge and dipole conservation, the paradigmatic setting for strong Hilbert-space fragmentation. Combining a replica tensor-network formulation for charge and dipole-conserving gates, which reaches the annealed R\'enyi-2 entanglement asymmetry up to $$L=128$$, with Hamiltonian simulations and an exactly solvable dissipative model, we uncover a higher-order symmetric quantum Mpemba effect: the charge and dipole asymmetries each display Mpemba-like crossings on parametrically distinct timescales. Resolving the state into frozen and active Krylov sectors reveals the mechanism: frozen fragments retain a finite asymmetry that obstructs full restoration, while active fragments host the relaxation responsible for the crossings. Fragmentation thus does not preclude the quantum Mpemba effect but reshapes it into frozen memory and active-fragment relaxation, providing a framework for the Mpemba phenomenology of higher-moment symmetries.
The classic Mpemba effect was noticed by a Tanzanian schoolboy in 1963 when he was making ice cream and found that the hot mix froze faster. His observation baffled many physicists.
The division into isolated pockets resembles the many-worlds interpretation: the system's past is preserved in separate branches of reality, like parallel universes.