This work investigates the quantum Mpemba effect in systems with strong Hilbert space fragmentation caused by simultaneous conservation of charge and dipole moment. Using tensor networks for the Rényi-2 entanglement asymmetry (up to L=128) and Hamiltonian simulations, a higher-order Mpemba effect is discovered: charge and dipole asymmetries exhibit crossings on parametrically different timescales. Analysis in frozen and active Krylov sectors showed that frozen fragments retain finite asymmetry, preventing full symmetry restoration, while active sectors are responsible for the relaxation that gives rise to the crossings. Thus, fragmentation does not eliminate the quantum Mpemba effect, but transforms it into a combination of frozen memory and active relaxation, setting the framework for Mpemba phenomena with higher symmetry moments.
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.
🎯 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.