First-Order Recoverability Collapse in Self-Referential Information Decoders
2026-06-23 • Information Theory
Information Theory
AI summaryⓘ
The authors analyze systems that process information and make irreversible decisions while constantly under pressure from incoming data. They model these systems as having limited capacity to handle information and show what happens when this capacity is exceeded, leading to failures that can't be easily fixed. They find that simply adding more capacity doesn't prevent problems unless the system carefully verifies each action, and they describe how these failures behave statistically, resembling certain patterns in physics. Their work provides a general framework to understand when and how such systems remain stable or fail under heavy workload.
nonequilibrium thermodynamicsirreversible actionfinite-capacity decoderrecoverabilityphase transitionbistabilitycascade dynamicsLandauer's principlestatistical mechanicsmetastability
Authors
Pieter van Rooyen
Abstract
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.