Geometric Entropy Principle: Horizon Thermodynamics and the Emergence of Physical Energy Scales

Geometric Entropy Principle (GEP) proposes that the hierarchy of fundamental energy scales in physics emerges from the finite holographic information capacity of the observable universe. Using the thermodynamics of the de Sitter horizon at the Gibbons–Hawking temperature, the paper defines a canonical ensemble of configurations of an information field on the holographic boundary. Maximizing Shannon entropy under a scale-invariant constraint yields a unique logarithmic ladder of vacuum phases, En = EPl N^ (-n/k), where N ~ 10¹22 is the holographic capacity of the universe and k ≈ 36 follows from the coarse-graining scale of semiclassical spacetime in loop quantum gravity. The resulting ladder reproduces the approximate positions of the GUT, leptogenesis, and electroweak scales to order-of-magnitude accuracy and predicts a new physical phase near 10⁵. 4 GeV (~250 TeV). As a possible microscopic realization, the information field is modeled as a nonlinear sigma model mapping spacetime into CP², whose topological sectors provide a candidate structure for the vacuum phases. The paper presents a programmatic framework linking horizon thermodynamics, holography, and the emergence of physical energy scales, and formulates several concrete open problems whose solution would complete the theory.