First-Order Recoverability Collapse in Self-Referential Information Decoders: The Operating Loop of an AI System as a Driven Nonequilibrium Steady State

Abstract

What kind of physical object is an artificial-intelligence system: a machine in the sense a refrigerator is -- dissipating free energy while holding an order imposed from outside -- or a dissipative structure in the sense a convection cell is -- an ordered state that exists only under throughput and loses stability past a critical drive? We argue the answer is split, as it is for the living cell and the star -- the trained artifact is a machine, quenched and storable; the operating loop is a dissipative structure in the informational sense -- and develop the framework in which the loop's classification becomes decidable. Modeling systems that couple inference to irreversible action as finite-capacity decoders under sustained informational driving, we characterize recoverable operation by a feasibility margin, local invertibility, and a stability diagnostic that diverges as capacity saturates. Making the feedback of uncertified output onto load explicit converts this continuous transition into a first-order one at mean-field level, sharpening in the fleet limit: lucid and collapsed states coexist in a cusp-organized bistable region with closed-form spinodals, collapse pre-empts the divergence, recovery is hysteretic, and for ungatedness alpha >= 1 load reduction alone cannot restore operation; reset restores only what is archived, making certification the operative stability lever. Cascades are subcritical branching with mean-field exponent 3/2 and a cutoff set by the grounded fraction of input. An instrumented real-workload pipeline experiment exhibits the collapse just below the spinodal computed from the measured service law, the backlog-delayed hysteretic recovery, and the cascade statistics. This supplies a statistical-mechanics account of the "metastable failures" documented in large-scale distributed systems, identifying recoverable dissipation as the stability criterion.