SDEL Quad Energy Framework: A Scale Dependent Emergent Model of Information, Interaction, Dynamic, and Coherence Energies

The Scale Dependent Emergent Law (SDEL) Quad Energy Framework proposes that physical reality can be modeled through four interdependent energetic forms: Information Energy EInfEInf, Interaction Energy EIEI, Dynamic Energy EDED, and Coherence Energy ECEC. Grounded in SDEL’s 34 axioms, these energies are treated as successive stages in a scale dependent cascade, beginning from a pre geometric informational substratum. Scale ss is defined as a dimensionless topological/computational parameter. Information Energy is linked to Landauer’s principle and mutual information, Interaction Energy is defined as a scale gradient (and optionally via a renormalization group derivative), Dynamic Energy represents usable work modulated by an efficiency factor (with optional Sagawa–Ueda bounds), and Coherence Energy stabilizes and unifies the previous three energies, with extensions based on multivariate mutual information (synergy) and stochastic RG flow. The model is presented as an effective description valid at specific scales, with qualitative numerical examples and suggested testable implications, consistent with SDEL’s non finality (Axiom 27).