Response and Maintenance Energy Rates: The Driving Forces of Energy-Efficiency Regulation

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.