The Theory of Entropicity (ToE) Sheds Light on String Theory, Quantum Field Theory, and the Casimir Effect: Strings and Branes are Vibrations of Information [Geometry] in the Entropic Field of ToE

Recent developments across holography, information geometry, and quantum gravity increasingly suggest that entropy and information are not auxiliary descriptors of physical systems but primary agents underlying geometric and dynamical structure. Building on this insight, the Theory of Entropicity (ToE) proposes that entropy 𝑆 ( 𝑥 ) is the fundamental dynamical field from which matter, forces, and spacetime emerge. In this framework, geometry becomes the macroscopic expression of informational curvature, quantum fields arise as localized perturbations of the entropic manifold, and vacuum phenomena such as the Casimir effect reflect constraints on informational flow rather than fluctuations of a physical vacuum. This paper develops a unified entropic reinterpretation of three major pillars of high‑energy physics. First, string theory is reformulated in terms of entropic vibrations: the vibrational spectra traditionally attributed to extended objects correspond to compactified oscillations of the entropic field, leading to natural entropic corrections to string masses and tensions. Second, quantum field theory is recast as an emergent description of the spectral and local dynamics of 𝑆 ( 𝑥 ) , with renormalization interpreted as the reorganization of informational degrees of freedom. Third, the Casimir effect is derived from first entropic principles, revealing that its characteristic 𝑎 − 4 scaling arises from entropic curvature pressure rather than zero‑point energy. By synthesizing insights from Bianconi’s metric relative entropy, Takayanagi’s pseudo‑entropy program, and classical information geometry, ToE provides a coherent entropic foundation from which string vibrations, quantum structure, spacetime curvature, and vacuum forces emerge as manifestations of a single informational field.