Entropy, Annealing, and the Continuity of Agency in Human–AI Systems

Adaptive systems that couple inference to irreversible commitment are governed by a rate-capacity law analogous to Shannon's: agency persists only while the induced informational flux Rself remains below the integrative capacity Cself. We define Recoverable Self-Coding (RSC), a structural framework in which the self - human, organizational, or artificial - is a self-decoder whose feasibility is tracked by a small set of measurable parameters: the capacity ratio CR = Rself/Cself, the margin M = Cself - Rself, the accessible-option entropy Hself, an exploration temperature T, and a finite integration horizon. Sustained CR > 1 makes state evolution non-invertible: options are eliminated faster than they can be reconstituted, and recovery cannot be restored by effort, intelligence, or optimization. We show that the parameters are directly estimable from open longitudinal event streams, verifying the construct on four open cohorts - synthetic health records (~1,900 units), the MIMIC-IV and eICU demonstration cohorts, and ~40,000 ICU stays from the PhysioNet/CinC 2019 sepsis challenge - where critically ill patients concentrate at the feasibility boundary CR ≈ 1 and outcome-labelled populations (sepsis; death in unit) sit measurably deeper into infeasibility without any fitted model. Applications are developed for healthcare capacity monitoring; for human agency under rate shocks - episodes, from a serious diagnosis to AI adoption, that abruptly multiply the induced flux against slow-adapting personal capacity; and for operational systems whose certification backlogs are directly observable. Annealing - regulated exploration followed by feasibility-paced consolidation - emerges as the admissible dynamics for staying recoverable under acceleration.