The Language Funnel Hypothesis: A Unified Physical Framework for Phase Transitions in the Acquisition of Biological and Artificial Intelligence

How biological brains seamlessly consolidate new linguistic structures while artificial neural networks suffer from catastrophic forgetting remains a central paradox in cognitive science. To resolve this, we propose the Language Funnel Hypothesis—a mechanistic framework that unifies psycholinguistics, non-equilibrium thermodynamics, and information theory. Moving beyond descriptive heuristics, this framework analogizes continuous L2 input to a high-entropy ``sand'' flux flowing through a cognitive funnel, where structural consolidation emerges as a non-linear phase transition into low-entropy ``stones.'' By introducing a dimensional architecture, we quantify instantaneous input as cognitive work density (W^2) and derive explicit equations for variance-weighted consolidation rates. In this system, net activation intensity is modulated by first-language (L1) interference (acting as systemic impedance), energetic thresholds (theta), and temporal signal instability. This approach yields four falsifiable predictions: (1) threshold-driven consolidation failures (the ``plateau''), (2) variance-locked efficiency collapse, (3) competitive impedance, and (4) a cubic scaling effect (T_{L2}^3) where doubling exposure time yields a deterministic eight-fold increase in crystallization velocity. Anchored by \textit{Gedankenexperiments}, the model establishes a deterministic metric for structural plasticity. Ultimately, the framework not only offers testable implications for L2 pedagogy but extrapolates these physical boundaries to address continual learning bottlenecks and alignment in artificial intelligence.