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 differential geometric model treating energy as a manifold-valued field. Extending classical tensor analysis to include Hodge duals, gauge-covariant derivatives, and boundary flows, this formulation aims to unify topological and thermodynamic aspects of quantum and gravitational systems. We present the governing PDEs, LaTeX TikZ-illustrated geometry, and explore implications from entropy dynamics in quantum information theory to brane-localized energy structures.{Correspondence and inquiries welcome.}