Entropy Collapse: Empirical Detection and Recovery Limits in AI Systems

Contemporary artificial intelligence systems increasingly rely on recursive feedback processes, including self-training, preference optimization, and algorithmic governance loops. Across these settings, practitioners report a recurring failure mode in which system behavior contracts, dominant patterns emerge, and corrective interventions lose effectiveness. While such phenomena are often attributed to convergence or over-optimization, there remains no general empirical criterion for declaring when a system has entered an irrecoverable state. This paper introduces a fully empirical system for detecting entropy collapse in feedback-driven AI systems. Collapse is defined operationally, not by low entropy alone, but by the failure of admissible interventions to restore diversity within a finite observation window. The framework relies exclusively on observable quantities, including empirical state distributions, Shannon entropy, dominance concentration, distributional displacement between iterations, and second-order change in displacement. A recovery-based threshold is constructed from repeated intervention experiments, yielding a system-specific limit beyond which collapse becomes statistically irreversible. An empirical demonstration is provided using a recursive AI setting, illustrating how collapse can be anticipated prior to full stagnation and formally declared once recovery probability falls below a prescribed tolerance. The same empirical indicators generalize naturally to socio-technical systems governed by feedback, offering a common language for diagnosing rigidity, adaptability loss, and governance failure. By grounding entropy collapse in measurable irrecoverability rather than descriptive convergence, the proposed system provides a practical tool for early warning, evaluation, and intervention in AI systems and their societal deployments.