Cognitive Phase Transitions: The Response Pool Equation and the Thermodynamics of Cognitive Meltdown

Scientific revolutions, cognitive insights, and belief revisions are not mysterious events---they are thermodynamic phase transitions. Building on the Universal Equation derived in the companion paper Model Energy Efficiency Ratio and the Universal Equation, this paper develops the complete dynamics of cognitive phase transitions, strictly grounded in EET Core Rules v4. 2. We introduce the Response Pool A (t), which accumulates unresolved prediction errors (anomalies) when the system operates below the Universal Equation boundary. Its dynamics are governed by the Response Pool Equation (Master Equation 2 of v4. 2): (t) dt = Ė (t) - A (t) ₃₄₂₀ₘ (), Ė is the anomaly power deficit and ₃₄₂₀ₘ () is an energy-ratio-dependent decay time. We propose the Kramers-EET Hypothesis to ground ₃₄₂₀ₘ () in activated barrier crossing. A Cognitive Meltdown---the cognitive analogue of a first-order phase transition---occurs when the accumulated response energy satisfies the Topological Meltdown Criterion: (t) Eb^melt or equivalently Ė > Ė₂ₑ₈ₓ = Eb^melt₃₄₂₀ₘ (). marks the moment of paradigm shift (Kuhn), insight (psychology), or catastrophic forgetting (AI). Crucially, the Asymmetry Law of Topological Barriers (Eb^melt Eb^form) from Postulate 3 explains the profound thermodynamic inertia of old paradigms. We distinguish three types of cognitive phase transitions---energy-level transitions, collapses, and thermal throttling---and analyze the Hierarchical Annealing process after meltdown, where the system follows a cooling schedule that depends on the nesting depth L of the cognitive model. Finally, we demonstrate the scale-free nature of the Response Pool Equation across neural plasticity, AI catastrophic forgetting, human behavior, and social revolutions. Four falsifiable predictions with explicit statistical power analysis are provided. Constitutional guardrails (Prohibited Moves 5, 8) are enforced.: Cognitive phase transitions; response pool equation; topological meltdown; Energy-Efficiency Theory; paradigm shift; annealing; barrier asymmetry