Title: Thermodynamics Constrains Life Systems to Rational Response Functions

AbstractLiving systems operate under fundamental thermodynamic constraints. We propose a minimal rational response function derived from three universal principles: saturation, diminishing energetic returns, and irreversible adaptation. The resulting function satisfies all constraints and emerges across molecular, neural, and behavioral scales. This framework unifies diverse biological phenomena—including Michaelis-Menten kinetics and predictive coding—under a compact thermodynamic formulation. It describes the deterministic, non-chaotic regime of biological systems and suggests a general mathematical language for adaptive responses in living systems.