Enterprise AI systems do not fail because of insufficient data, weak tuning, or flawed deployment pipelines. They fail because information behaves like energy: it accumulates entropy, dissipates meaning, and destabilizes unless constrained by structural anchors. This paper introduces Informational Thermodynamics, a physics-inspired theoretical framework that models semantic degradation in recursive cognitive systems. Rather than treating AI failure as a temporal or statistical event, the study reframes collapse as a velocity phenomenon governed by a domain-specific drift constant (λ). Across finance, law, and medicine, systems traverse the same universal recursive sequence (C₀–C₄), but at markedly different speeds determined by epistemic architecture rather than model design. Using a structural analysis of 100 peer-reviewed documents, the study derives λ from five parameters: semantic density, decision velocity, interpretive tolerance, error asymmetry, and redundancy. The results show that industries do not differ in when collapse occurs, but in how fast semantic entropy accelerates once recursion begins. High-velocity domains exhibit rapid deterioration masked by rising fluency, while redundancy-rich domains decay more slowly. The paper positions Enterprise Semantic Integrity (ESI) as an entropy-regulation mechanism capable of reducing effective collapse velocity without eliminating entropy itself. The contribution establishes Informational Thermodynamics as a foundational planning science for AI governance, organizational stability, and human–AI decision systems, and serves as a theoretical cornerstone for the forthcoming Enterprise Semantic Integrity (ESI) standard.