ABSTRACT The High Entropy Predictive Organization Efficiency (HEPOE) theory established the fundamental thermodynamic boundaries of neurodivergent cognition through the Predictive Solvency Inequality. This technical update expands the framework into a dynamic temporal model, introducing the Brezolin Solvency Integral. We propose that neurocognitive exhaustion and the phenomenon of "Brain Fog" are emergent properties of a negative energy balance in High-Fidelity architectures, specifically within the Sentinel Phenotype. The model is presented as an etiologically agnostic Shell Theory (Meta-Architecture), where genetic, enzymatic, and neuroinflammatory variables are treated as coefficients of Systemic Friction (Ω). By applying Landauer’s Principle, we demonstrate that "Brain Fog" functions as a critical "thermal circuit breaker" necessary to prevent glutamate-mediated excitotoxicity resulting from the heat dissipation inherent in high-fidelity informational erasure. Furthermore, we introduce the Recovery Integral to quantify the impact of Residual Insolvency, providing a mathematical justification for the clinical necessity of sensory isolation and restorative "cooling" periods in twice-exceptional (2e) populations. Keywords: HEPOE Theory. Bioenergetic Solvency. Dynamic Integral. Information Thermodynamics. Brain Fog. Sentinel Phenotype. Metabolic Friction.