A state-resonant energy transmission law for energy materials and beyond

Energy flow in materials is conventionally described as transport driven by particle migration, scattering, or diffusion. Here we show that in confined and field-structured systems, energy transmission is instead governed by energy-state accessibility and resonance. We introduce the State-Resonant Energy Transmission Law (SRETL), Φ = ν 0R (E ), where Φ is the macroscopic energy flux, ν 0 is an intrinsic activation frequency, and R (E ) is a dimensionless transmission function that depends on the accessible energy states E . The SRETL unifies classical migration-limited transport and wave-like, resonance-mediated transmission as complementary regime limits of a single governing principle. Applied to ultrafast carrier-lattice dynamics, the framework reinterprets experimentally observed phase delays as waiting times for state-resonant transmission, providing a concrete route to extract transmission functions from time-resolved measurements. Beyond electronic systems, the SRETL establishes a general paradigm for engineering energy transmission in ionic and protonic materials through controlled state accessibility rather than reduced resistance.