The entropic Inevitability of localized Intelligence: theoretical foundations for the transition from scalable to dense cognitive architectures

Abstract The contemporary paradigm of artificial intelligence development, predicated upon extensive scaling of computational resources and training data volumes (so-called “Greedy AI”), approaches fundamental thermodynamic and algorithmic efficiency limits. This work proves that the transition to compact, energy-efficient systems with high abstraction density (the “Green Paradigm”) constitutes not a strategic choice, but a physical inevitability mandated by the laws of information thermodynamics and algorithmic complexity theory. Building upon the Minimum Description Length (MDL) principle, Landauer’s bound, and Friston’s Free Energy Principle, we formalize the concept of vitality in intelligent systems—their capacity for structural rule synthesis under severe resource constraints. We demonstrate that true AI capability is determined not by parameter count |θ|, but by the degree of algorithmic information compression K(x), and that the ratio K(x)/|θ| → 0 under unconstrained scaling represents a mathematical pathology. The paper provides rigorous proofs of the energetic unsustainability of cloud architectures upon reaching critical complexity, quantitative analysis of approximation limits in the context of Kolmogorov complexity, and formulation of the Structural Autonomy Axiom as a criterion for genuine system intelligence. The proposed theoretical framework establishes a mathematical foundation for creating autonomous intelligent agents capable of operating on local user devices while maintaining cognitive capabilities comparable to contemporary large-scale models.