Nonmetric Geometric and Quantum Information Flows and Evolution of Black Hole and Cosmological Solutions in f(Q) Gravity Versus General Relativity

ABSTRACT Nonmetric and nonholonomic deformations of Einstein–Dirac–Maxwell systems, together with their cosmological implications in metric‐affine geometries and modified gravity theories (MGTs), have been explored in a series of recent works; however, classical and quantum information—theoretic interpretations of nonmetric geometries, and their connections to nonstandard particle physics and MGTs, remain largely undeveloped. In this work, we formulate nonmetric geometric and (quantum) information thermodynamic frameworks—referred to as geometric information flows (GIF) and quantum geometric information flows (QGIF)—within which metric‐affine gravity models, including f(Q) gravity, can be derived as particular classes of nonmetric Ricci solitons. We introduce generalized definitions and inequalities for relative entropy, mutual information, and entanglement in terms of nonholonomic geometric variables, and show that the corresponding nonmetric geometric flow equations can be decoupled and integrated in generic off‐diagonal form using the anholonomic frame and connection deformation method. This formalism enables the explicit construction of exact and parametric solutions and the computation of associated geometric and informational thermodynamic variables, including physically relevant examples describing nonmetric deformations of quasi‐stationary black hole‐type configurations into locally anisotropic cosmological solutions. We conclude that nonmetric GIF and QGIF thermodynamic variables provide a unifying framework for identifying classes of MGTs suitable for quantum–computational modeling of gravitational and cosmological phenomena, capable of describing accelerating cosmologies and astrophysical objects via off‐diagonal configurations in general relativity and extensions such as f(Q) gravity, with further developments to explore connections to quantum information theory through nonmetric generalizations of Perelman's W‐entropy.