Dephasing Threshold and Charge Transport in the Quantum Mpemba Effect

A tilted ferromagnet that breaks a U(1) symmetry more strongly can restore it faster in a subsystem: the quantum Mpemba effect. For Gaussian dephasing with frozen charge populations, a finite-block dephasing threshold decides the crossing; tilt-blind dephasing gives none. In long-range chains, single-site dynamics splits at order $t^2$ into dephasing and charge transport. Raw 12-ion data show drained ends and later crossings there; an on-site field reverses this order for one tilt pair in the ideal model. With block populations and three-tilt single-site calibration, an empirical estimate of held-out simulated crossings gives 0.06 ms pooled median error across 719 dependent evaluations for the sampled 12-ion chains with interaction exponents 0.5 and 1, their coupling perturbations, and two reconstructed 51-ion models.