The Operational Coherence Framework (OCOF) proposes a unified theoretical model linking information thermodynamics, cognitive science, and artificial intelligence. Building upon five axioms—Boundary Persistence, Predictive Inference, Semantic Value, Policy Integration, and Systemic Coherence—OCOF suggests that cognition and intelligence emerge through an entropic negotiation between informational precision and semantic differentiation. The framework formalizes semantic value as S = I × σ, where I denotes mutual information and σ represents semantic potential, thereby extending concepts from the Free Energy Principle by introducing meaning as an operational variable. This study employs a theoretical modeling approach supported by computational simulations and synthetic data analysis. It does not involve human participants or empirical biological experimentation. Through this structure, OCOF aims to bridge the physical basis of information with higher-order cognitive functions, offering a computationally implementable framework. The theory is supported by a comparative literature review and operational appendices covering mathematical formulation, simulation-based psychological modeling, and ethical integration. OCOF aims to establish a measurable link between informational boundaries, semantic integration, and adaptive intelligence, contributing to interdisciplinary discussions in physics and cognitive science.