Average Action Efficiency and Positive Feedback in the Coevolution of Dynamics and Structure

Self-organizing open systems, sustained by continuous fluxes between sources and sinks, convert stochastic motion into structured efficiency, yet a first-principles explanation of this transformation remains elusive. We derive the time-dependent Average Action Efficiency (AAE)—defined as events per total action—from a stochastic–dissipative least-action principle formulated within the Onsager–Machlup and Maximum Caliber path-ensemble frameworks. The resulting Lyapunov-type identity links the monotonic rise of AAE to the variance of action and to the rate of noise reduction, delineating growth, saturation, and decay regimes. Self-organization emerges from a reciprocal feedback between dynamics and structure: the stochastic dynamics concentrates trajectories around low-action paths, while the resulting structure, through the evolving feedback precision parameter β(t), modulates subsequent dynamics. This self-reinforcing coupling drives a monotonic increase of the dimensionless Average Action Efficiency α(t)=η/ t, providing a quantitative measure of organizational growth. In the deterministic limit, the theory recovers Hamilton’s Principle. The increase of AAE corresponds to a decrease in path entropy, yielding an information-theoretic complement to the Maximum Entropy Production and Prigogine–Onsager variational formalisms. The framework applies to open, stochastic, feedback-driven systems that satisfy explicit regularity conditions. In Part II, agent-based ant-foraging simulations confirm sigmoidal AAE growth, plateau formation, and robustness under perturbations. Because empirical AAE requires only event counts and integrated action, it offers a lightweight metric and design rule for feedback-controlled self-organization across physical, chemical, biological, and active-matter systems.