Energy-Space Gravity: Toward a Unified Entropic Framework for Gravitation and Quantum Geometry

We present a reformulation of gravity in which spacetime curvature emerges from entropy gradients in a generalized energy-space manifold, eliminating the need for fundamental time. Building on thermodynamic principles, we derive entropy-corrected Einstein field equations and modified geodesic motion from a covariant variational principle. The resulting framework predicts gravitational effects as a consequence of entropy divergence, offering a unified perspective on black hole thermodynamics, cosmic acceleration, and quantum gravity. Energy-space gravity naturally explains gravitational wave dispersion, black hole horizon corrections, and deviations in the CMB power spectrum without invoking dark energy. We propose concrete experimental and observational tests—including pulsar timing anomalies, Casimir effect shifts, entropy-driven gravitational lensing, and entropy-modulated nucleosynthesis—to validate the theory. The framework integrates with loop quantum gravity and holography, suggesting a deeper entropic origin of quantum geometry. This work establishes energy-space gravity as a testable, time-free extension of General Relativity, capable of resolving longstanding tensions between gravitation, thermodynamics, and quantum theory.