ENTRO-QUANTUM: Entropic Collapse in Probabilistic State Spaces of Artificial Intelligence

ENTRO-QUANTUM (E-LAB-07) introduces a quantum-inspired probabilistic framework for modeling entropy dynamics in artificial intelligence systems operating near instability boundaries.Classical entropy models represent system state as a deterministic scalar. This work demonstrates that such representations fail to capture critical phenomena observed in high-dimensional AI systems, including sudden collapse events, non-local correlations, and measurement-induced instability.To address these limitations, this study defines the Entropic Wavefunction Ψ-W(s,t), a complex-valued probability amplitude over stability states. The framework extends classical entropy dynamics into a probabilistic regime governed by an Entropic Schrödinger Equation, enabling the modeling of:Superposition of stability statesMeasurement-induced collapseInformational entanglement across distributed systemsDiscontinuous entropy transitions via Quantum Jump OperatorsA formal Entropic Uncertainty Principle is derived, establishing a lower bound between measurement precision and disturbance. This result leads to the formulation of the Silent Observer Protocol, an adaptive monitoring strategy that minimizes collapse risk in near-critical systems.The framework unifies and extends previous components of the EntropyLab Research Program (E-LAB-01 through E-LAB-06), recovering classical entropy dynamics as a limiting case of wavefunction collapse.The paper provides a complete mathematical formalism, theoretical predictions (P1–P5), and a simulation-based validation strategy using Monte Carlo trajectory methods.This work is theoretical and computational in nature. All results are derived from first principles and validated through controlled simulations. No human or real-world datasets are involved.ENTRO-QUANTUM establishes a new modeling paradigm for AI stability under uncertainty, bridging deterministic control architectures and probabilistic dynamics inspired by quantum mechanics. This work is preregistered on OSF Registries: Registration DOI: 10.17605/OSF.IO/APZ7Y Registry: OSF Registries Registration Type: Preregistration Date Registered: April 10, 2026 License: CC-BY 4.0