Non-Reversibility, Gate Admissibility, and Ratchets

Non-reversibility is not a quirk of implementation; it is a design law. We formalize ratchets as one-way updates that trade symmetry for memory, define gate admissibility as the local criterion that ensures updates respect invariant structure under quotient flows, and prove closure and stability theorems that make the law computational. The core claim is simple: in systems that must remain intelligible under coarse-graining, only a small set of non-reversible gates are admissible, and their compositions preserve safety and predictability while allowing capability growth along controlled, one-way directions. We supply (i) a categorical/measure-theoretic semantics for gates as decision kernels on quotient flows; (ii) an admissibility calculus driven by Fisher-curvature and spectral tilts; (iii) Lyapunov–drift and regeneration guarantees for on-line operation; (iv) Murphy horizons and flow centrality as planning instruments; (v) falsifiable predictions and stress tests. Along the way we connect to canonical-form concentration, spectral large deviations, and sheaf-theoretic obstructions, consolidating non-reversibility as an organizing principle rather than an afterthought.