Accessibility-Loss Events in Gaussian Open Quantum Systems: A Structural Framework

This work develops a structural framework for accessibility-loss events in open-system decoherence under fixed control. Instead of focusing on externally tuned filter-function changes, the analysis centers on the reduced decoherence functional χ(T), which is decomposed into positive effective contributions within an additive Gaussian description. An accessibility-loss event is defined as a fixed-control transition in which one effective contribution ceases to participate within the coherence-estimation window. The primary invariant of the event is the event amplitude f(T)=1−χpost(T)χpre(T), which measures the lost fraction of the pre-event decoherence functional. We show that f(T) is scale-invariant, depends only on participation structure, and that event existence is equivalent to f(T)>0. Numerical ratios such as pre/post coherence-time ratios are therefore derived quantities, not defining features of the event. A sharp-switch limit is derived: when the suppression timescale is short compared with the estimation window and the remaining background varies more slowly, a smooth microscopic suppression appears as an effectively discontinuous jump in window-averaged observables. This leads to a two-layer falsification structure: (1) falsification of event existence (whether f>0), and (2) falsification of subclass-specific benchmark values. As an illustration, we identify a symmetric normalized subclass in which the fluctuation-sector contributions satisfy a normalized isotropic structure, yielding f=14,R=TpostTpre=43 within the single-rate regime. These values are not universal constants of open-system decoherence but benchmark invariants of this restricted structural subclass. The framework clarifies that decoherence encodes not only spectral and control information but also participation structure—which effective contributions are active within the observation window and when that participation changes. Accessibility-loss events thus represent structurally identifiable transitions in reduced decoherence geometry, independent of microscopic realization.