Gradient Entropy Principle (GEP): Information Gradients as the Origin of Gravitation

This work introduces the Gradient Entropy Principle (GEP), a theoretical framework proposing that gravitation may emerge from spatial gradients of information encoded in spacetime. In this approach, matter does not directly generate spacetime curvature; instead, it generates a scalar information field whose gradients determine the gravitational field and the resulting spacetime geometry. The paper presents the basic postulates of the framework, derives the weak-field equation for the information field, and introduces a spacetime metric that reproduces the weak-field limit of the Schwarzschild solution. Using this formulation, the model reproduces the classical tests of general relativity in the weak-field regime, including gravitational redshift, light deflection, and perihelion precession. The framework also connects naturally with black hole thermodynamics and the Bekenstein–Hawking entropy relation, suggesting that black holes may correspond to configurations in which the informational capacity of spacetime becomes saturated. In this view, gravitation can be interpreted as a geometric response of spacetime to gradients in its underlying informational structure. The Gradient Entropy Principle is presented as a working hypothesis at the level of linearised general relativity, intended as a conceptual step toward a deeper connection between gravitation, thermodynamics, and information theory. Further work is required to develop a fully covariant formulation and to identify the microscopic degrees of freedom underlying the proposed information field.