The Two Fundamental Forms of Energy: Free State and Constrained State — A First-Principles Reconstruction from Energy-Efficiency Theory

This paper systematically expounds the two fundamental forms of energy in Energy-Efficiency Theory (EET): the free state (continuously distributed, propagating at light speed, e.g., waves and fields) and the constrained state (localized, stable, subluminal, e.g., particles and matter). It provides rigorous definitions, mathematical characterizations, and quantitative models of state transitions. Using this framework, it unifies wave-particle duality, quantum measurement collapse, and the mass-energy equivalence, with experimental validation from the carbon-12 nucleus. It further engages with contemporary structural realism and information ontology. This work establishes the physical ontological foundation of EET.