Stochastic-dissipative least-action framework for self-organizing biological systems, Part I: Variational rationale and Lyapunov-type behavior.

How and why do complex chemical and biological systems self-organize into ordered states far from thermodynamic equilibrium? Despite advances in thermodynamics, kinetics, and information theory, a unifying principle that links organization and efficiency across scales has remained elusive. In open systems, productive-event trajectories are conditioned on starting at a source and ending at a sink. This work proposes a stochastic-dissipative least-action triad framework in which (i) a path-ensemble weighting biases trajectories by their action cost, (ii) feedback processes sharpen this distribution, and (iii) the ensemble evolves toward a least-average-action attractor, decreasing during self-organization and increasing during decay. A parametric cross-scale metric-Average Action Efficiency (AAE)-is defined, which is inversely proportional to the average action per productive event. Under reinforcing feedback, identities derived from the exponential-family path measure show that the average action decreases and AAE rises monotonically. In future extensions, this formulation could help bridge quantum, classical, and biological regimes while remaining computationally tractable, because its empirical version relies on aggregate energetic and timing data rather than enumerating individual trajectories. AAE reaches a local maximum at a non-equilibrium steady state under fixed operational context, consistent with the present formulation, and connections to thermodynamic and informational measures are made. A companion article (Part II) details empirical estimation strategies and applications (Georgiev, 2025a).