Energy as a Manifold Field: Geometry, Entropy, and Quantum Flow

Energy as a Manifold Field: Geometry, Entropy, and Quantum Flow author Edwin J. Vening, orcid 0000-0002-1183-2158, email [email protected] We propose a model treating energy as a manifold-valued 1-form on a 4D Lorentzian manifold, unifying topological, thermodynamic, and quantum aspects. Using Hodge duals, gauge-covariant derivatives, and boundary fluxes, we derive equations governing entropy dynamics and introduce thevCausal Shadow Flux (CSF)}, quantifying entropy across timelike boundaries. Holographic tensor networks {Bao2024} and causal set theory {Sorkin2025} refine CSF calculations. The model predicts measurable entropy production in driven quantum systems, applicable to quantum optics, cosmology, and computing. Visualizations and simulations validate the framework.{Correspondence and inquiries welcome.}