Entropy as Information Curvature: Unifying Matter, Gauge Fields, and Gravitation through Entropic Geometry

We present a unified theoretical framework in which matter, gauge fields, and gravitation emerge as manifestations of an underlying entropic information geometry. The formalism is constructed on a diagram–Hilbert space, where topological projections encode correlations between quantum degrees of freedom, and entropy acts as the generating functional of field dynamics. Within this setting, the Fisher information metric defines an entropic curvature tensor whose extremization yields the effective Einstein and Yang–Mills equations as equilibrium conditions of informational entropy. Gravitational coupling emerges from the topological entropy density associated with information flow between matter sectors, while gauge interactions correspond to localized curvature defects in the entropic manifold. The Bekenstein–Hawking entropy and holographic bounds appear as limiting configurations of the same information potential, providing a continuous transition from black hole thermodynamics to the standard-model regime. The framework naturally accounts for mass generation through effective entropic projections within the diagram–Hilbert space, linking the structure of the Standard Model to topological invariants of the entropic geometry. This approach establishes a self-consistent and renormalizable unification of gravity and gauge fields, grounded in the informational and thermodynamic origin of physical law.