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AI maturity frameworks have proven effective at benchmarking organizational progress in artificial intelligence adoption, yet they remain fundamentally descriptive and static. They identify who succeeds, but offer limited explanatory power for why stability degrades under scale, why investment returns diminish, or why early success frequently precedes systemic failure. This gap reflects the absence of a dynamic governing layer capable of modeling time-dependent instability in AI capability systems. This working paper operationalizes Knowledge Thermodynamics (KT) as a dynamic extension of existing AI maturity frameworks. KT treats organizational AI adoption as a thermodynamically constrained process in which energy investment, entropy production, and dissipation capacity jointly determine system stability. By mapping KT variables onto an established AI maturity framework, the study transforms static maturity classifications into a continuous phase-space model that represents growth trajectories, stability thresholds, and collapse dynamics. The resulting Knowledge Thermodynamics Maturity Model (KTMM) introduces constructs including entropy accumulation, collapse velocity, and efficiency decay to explain observed patterns: skewed maturity distributions, diminishing returns on AI investment, governance-dependent stability, and scaling-induced failure. The analysis does not claim causal validation. Instead, it evaluates qualitative alignment between KTMM predictions and empirical patterns reported in large-scale AI maturity research, demonstrating explanatory adequacy as the appropriate epistemic standard at this stage of framework development. The contribution of this work is methodological rather than prescriptive. It demonstrates how an abstract governing framework can be operationalized without premature quantification, providing a diagnostic lens for pre-collapse observability in AI maturity assessment. The paper establishes boundary conditions, limitations, and four future research trajectories: longitudinal validation, measurement instrumentation, integration with financial and risk models, and cross-domain generalization. This preprint contributes methods and modeling foundations to the broader Enterprise Semantic Integrity (ESI) research program and the AiSEON Research Initiative's ongoing work in Knowledge Thermodynamics, Conversational Thermodynamics, and the CSID diagnostic family.