Divergence Geometry of Quantum Multi-Mpemba Effects
Abstract
Whether a quantum Mpemba effect occurs can depend on how distance from stationarity is measured. We show that agreement across normalized operator-convex Petz divergences is decided by a one-parameter $χ^2$ profile. Its sign fixes the common order, alternating sign margins guarantee repeated crossings, and finite dimension yields a polynomial positivity test. The same profile explains diagnostic-independent late-time order for a simple real slow mode and isolates coherence as the local source of diagnostic dependence. In a trapped-ion qutrit ideal model, the reported preparation gives diagnostic-selective crossings, while a nearby preparation is a floating-point candidate for two family-wide reversals. The framework turns diagnostic robustness into a tractable control problem.