First-Order Recoverability Collapse in Self-Referential Information Decoders

We study adaptive systems coupling inference to irreversible action under sustained nonequilibrium driving.

Treating information processing as a thermodynamic load, we model them as finite-capacity decoders whose irreversible commitments eliminate counterfactual options, and characterize recoverable operation by a feasibility margin and a stability diagnostic fixing when irreversible action is admissible.

Under sustained overload -- induced flux exceeding effective integrative capacity -- loss of recoverability and divergence of the diagnostic arise as structural consequences of capacity saturation, independent of optimization objective, control policy, or substrate.

Added capacity alone does not restore recoverability: absent certification or gating, higher throughput accelerates non-recoverable loss, with high-throughput AI a concrete application.

Making the feedback explicit -- each uncertified commitment spawning on average alpha new candidates -- turns the continuous transition first-order: lucid and collapsed states coexist in a cusp-organized bistable region with closed-form spinodals, collapse pre-empts the continuous divergence at finite stability ratio, recovery is hysteretic, and for alpha >= 1 load reduction alone cannot restore operation.

Cascade sizes are bounded by the grounded fraction of input: a genealogy-times-congestion factorization sets a cutoff that grows as grounding shrinks, with the mean-field exponent tau = 3/2 recovered away from the boundary and each cascade carrying a Landauer-priced burst of synthetic entropy; event-driven simulations confirm the cutoff law and phase structure.

This supplies the statistical mechanics of the metastable failures seen in distributed systems.

The analysis is constraint-based and substrate-agnostic, establishing recoverable dissipation as a necessary criterion for decoder stability in high-flux regimes.