The Theory of Entropicity (ToE) Goes Beyond Holographic Pseudo-Entropy: From Boundary Diagnostics to a Universal Entropic Field Theory

The recent work of Takayanagi, Kusuki, and Tamaoka introduces holographic pseudo‑entropy in non‑unitary CFT 2 and shows a striking correspondence: the first law of pseudo‑entropy is dual to the linearized Einstein equation in three‑dimensional de Sitter space once complexified extremal surfaces are allowed in the bulk. Variations of pseudo‑entropy also satisfy a Klein–Gordon equation on the kinematical space dS 2 , giving rise to an emergent time structure from an Euclidean boundary theory. In this paper, we argue that although the holographic pseudo‑entropy program provides a valuable boundary diagnostic of gravitational dynamics, it remains a restricted kinematical construction tied to holography, non‑unitary conformal field theories, and perturbative de Sitter gravity. By contrast, the Theory of Entropicity (ToE) treats entropy 𝑆 ( 𝑥 ) as the fundamental physical field, equipped with both a local variational principle (the Local Obidi Action) and a spectral variational principle (the Spectral Obidi Action). These actions yield the Master Entropic Equation, entropic geodesics, irreversible dynamics, and a unified description of gravity, time, quantum processes, and information geometry. The goal of this work is threefold. First, we present a clear exposition of the Takayanagi–Kusuki–Tamaoka framework. Second, we develop ToE as a universal entropic field theory whose dynamics extend beyond the holographic pseudo‑entropy correspondence. Third, we show how ToE absorbs pseudo‑entropy as a boundary manifestation of a deeper entropic field, explaining why pseudo‑entropy captures only the linearized sector of gravitational physics while ToE provides a fully nonlinear, time‑asymmetric, information‑geometric unification.