Structured Quantum State Evolution: Exploring Entropy-Guided Dynamics as an Alternative to Standard Decoherence Models

This theoretical physics paper proposes a mathematically rigorous framework for quantum state evolution that incorporates entropy-guided dynamics as a potential complement to standard environmental decoherence models. The work develops complete mathematical foundations using completely positive trace-preserving (CPTP) channels with explicit Kraus operators for hypothetical information-theoretic processes that may influence quantum system behavior beyond purely stochastic environmental interactions. Theoretical contributions include: Mathematically rigorous CPTP formalism with explicit Kraus operators for entropy-guided quantum dynamics Testable predictions that differ from both Lindbladian decoherence and gravitational collapse models Scale-dependent theoretical framework for quantum state evolution (2-20+ qubit systems) Experimental observations from real quantum hardware showing structured entropy distributions Analysis of experimental signatures across multiple quantum platforms (IBM, IonQ) Mathematical framework development: Complete entropy-guided master equation with CPTP channel representation Rigorous constraint encoding and multi-clause extensions for complex problems Circuit-level realization through Stinespring dilation and ancilla implementations Coherence Stabilization Rate (CSR) and entropy bias parameters as experimental observables Platform-independent predictions for structured quantum evolution patterns Experimental validation: Structured entropy measurements across IBM Sherbrooke, IBM Toronto, IonQ Harmony, and IonQ Aria platforms Consistent entropy reduction patterns in quantum circuits (7-10 bits for 8-12 qubit systems) Non-uniform collapse distributions favoring low-entropy configurations Reproducible results across independent hardware runs and problem classes This paper develops the theoretical foundation for entropy-guided quantum dynamics, introducing a CPTP channel model with constraint-consistent attractors and testable predictions for non-exponential decay and structured collapse. Companion work: Experimental validation and hardware benchmarks implementing this model are presented in Adaptive Quantum Circuit Architecture for Combinatorial Optimization (Knudsen 2025b), available at https://zenodo.org/records/16865582 Important note: While this framework is now mathematically rigorous and consistent with quantum mechanical principles, experimental observations require independent validation by other research groups. Alternative explanations for observed phenomena remain possible and should be investigated. Target audience: Theoretical physicists, quantum foundations researchers, quantum information theorists, and experimental quantum computing researchers interested in alternative approaches to the quantum-to-classical transition and novel quantum circuit architectures. All mathematical frameworks, experimental protocols, complete datasets, and analysis methods are provided for scientific scrutiny, independent validation, and further theoretical development by the research community. © 2025 Kristopher Knudsen / Axion Metrics LLC. This work is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).You are free to share, adapt, and build upon this work for any purpose, provided appropriate credit is given.License details: https://creativecommons.org/licenses/by/4.0/ Contact: [email protected]