The Rate Inheritance Principle: From Static Correlations to Dynamical Decoherence Rates

In gapped open quantum systems with localized couplings, static correlations across an operational interface of width eps are exponentially suppressed by the mass gap. Independently, the energetic cost of maintaining quantum coherence is governed by the rate at which coherence is lost under uncontrolled dynamics. The Rate Inheritance Principle (RIP) is the hypothesis connecting the two: effective coherence-loss rates inherit the suppression envelope of static correlations across the interface. We distinguish a weak upper-envelope form — stated here as a short proved lemma under explicit integrability hypotheses — from a stronger envelope-class conjecture, and we record what is now known: the strong form is derived, with a frequency-resolved exponent, in an exactly solvable quasi-free local-sink class, where the rate inherits the square of the static amplitude envelope, kappa(eps) proportional to e^(-2 q(omega_b) eps) — confirming the squared-envelope caveat anticipated in v1 — and it fails through near-zero-frequency channels within the secular Davies model class, whose delocalized jump operators sustain a persistent rate floor. Version 1's surrogate decay-curve evidence is withdrawn: it belonged to the uncontrolled proxy class whose failure mode was exposed by the critical-point control of the companion paper, and it is replaced here by the exact Liouvillian-rapidity evidence. Failure modes (now including secular delocalization), a proxy-validated falsification protocol, and the conditional operational consequences for the quantum-classical resource boundary are stated with explicit scope.