Record-based onset of irreversibility in continuously monitored open quantum systems

We develop a calibration-based framework for effective irreversibility in continuously monitored open quantum systems. The central quantity is Irec(t)=DKL(P1(t)‖P0(t)), the Kullback–Leibler divergence between calibrated measurement-record laws under two controlled branches. Within the equal-covariance Gaussian class, Irec(t) is deterministic for fixed record laws, is computable from Kalman-filter innovations, and obeys an exact master curve for minimum branch-discrimination error. The trajectory-level log-likelihood ratio Λ(t) is stochastic: a candidate onset location t× begins a sustained evidence interval, whereas a causal declaration is available only at tdec, after the interval has been verified. Thus, Idec = Irec(tdec) is distributed across trajectories, although Irec(t) is deterministic at a fixed time. A calibrated reference-register construction assigns a one-nat excess-free-energy reference to the stored record. The primary new protocol result is that, in information time u = Irec(t), a hold interval specified in accumulated-information units yields a rate-invariant declaration distribution within the Gaussian benchmark, whereas a fixed physical-time hold interval generally does not. As a model-specific physical corollary, for pure coherent output pointers and a complete matched homodyne record, residual branch coherence obeys Cdet(t) = exp[−Irec(t)/4]; selecting Cdet = 1/2 gives the illustrative marker Irec = 4 ln 2 nats. For incomplete detected records, the mapping acquires an effective-efficiency correction. In practical terms, the framework tells an experimenter when a continuously recorded signal has acquired stable evidence and how that declaration changes as measurement quality varies. We also derive the deterministic reference-time correction for time-dependent information rates and state experimentally testable failure criteria.