A Systems-Theoretic Framework for the Emergence of Adaptive Control:The Biological Principle of Least Action (BPLA)

A Systems-Theoretic Framework for the Emergence of Adaptive Control: The Biological Principle of Least Action (BPLA) This paper presents a formal axiomatic framework for replicating systems operating under non-equilibrium thermodynamic constraints. From four foundational axioms, a sequence of theorems derives the necessary existence of two structurally distinct metabolic pathways — a sensing pathway and a balancing pathway — as mathematical necessities for persistence, not biological assumptions. From these theorems, the Biological Action Functional is derived, whose minimization yields the BPLA equation: a predictive optimal control law decomposing adaptive behavior into three irreducible components — Capacity, Direction, and Urgency. The framework is validated via post-hoc statistical analysis of naive run-and-tumble agents in silico. The Urgency term emerges as a decisive selection filter exclusive to surviving lineages (p < 10⁻⁴⁴), confirming that adaptive agency is not a programmed biological invention but a necessary mathematical consequence of physical persistence.