This paper develops a comprehensive framework for the two fundamental energy allocation rates—the response energy accumulation rate E˙respE˙resp and the maintenance energy recovery rate E˙mainE˙main—that drive all adaptive non-equilibrium systems. The framework is part of Ben-Shi Dynamics, the kinetic core of Energy-Efficiency Theory (EET), which comprises the Energy-Efficiency Regulator (structure), the two energy rates (dynamics), and Yang's Ben-Shi Sliding equation (macroscopic evolution). Grounded in the three axioms of EET and aligned with the official EET specification 1, we define the physical origins of the two rates, derive their constraints from Axioms II and III, and establish cross-scale scaling relations: E˙main∝M3/4E˙main∝M3/4 and E˙resp∝M0.85±0.05E˙resp∝M0.85±0.05 across hierarchical levels from cellular to societal scales. We provide detailed, replicable measurement protocols for each rate, ensuring genuine falsifiability. The relation between the two rates and the Energy-Efficiency Regulator is made explicit, and their role in Yang's Ben-Shi Sliding equation is derived from first principles. The framework yields four testable predictions with quantitative thresholds and strict falsification criteria. This work completes Ben-Shi Dynamics, providing the complete dynamical foundation for non-equilibrium systems. References:1 Yang, H. (2026). Energy-Efficiency Theory (EET): Axioms and Core Concepts. Zenodo. DOI: 10.5281/zenodo.19282413.2 Yang, H. (2026). Yang's Ben-Shi Sliding: A Dynamical Framework for Conservation-Expansion Balance. Zenodo. DOI: 10.5281/zenodo.19284740.
Hongpu Yang (Thu,) studied this question.