Operational Copy Time and Audited Closure: A Locality–Mixing Separation Diagnostic for Open Quantum Dynamics

We develop an operational certification framework for micro–macro modeling in local quantum systems. Audited closure is defined as a uniform discrepancy bound between microscopic and surrogate predictions over a declared observable suite on a declared domain of states. A receiver-region copy time τ_copy(η;A→B) is defined as the earliest time at which a finite receiver region B can distinguish—at trace-distance threshold η—a localized perturbation supported on A. Under explicit Lieb–Robinson hypotheses for Hamiltonian or Lindbladian generators, we derive an exponential receiver distinguishability envelope and an explicit time-to-threshold lower bound, including the regime η≥Γ where the threshold is provably never reached and τ_copy=+∞. As an achieved-closure demonstration, we analyze a split-step quantum walk lifted to quasi-free lattice fermions and provide computable dispersion and two-point density audit bounds on a band-limited quasi-free domain. As a signature contribution beyond a repackaging of locality, we prove a locality–mixing separation theorem for primitive Lindbladians with a log-Sobolev (or mixing) rate λ: the receiver distinguishability is bounded by the minimum of a ballistic LR tail and an intrinsic mixing contraction, yielding a measurable crossover time and an operational separation between unitary and dissipative dynamics.