We present a novel derivation of the perihelion precession (shift) of Mercury using the Entropic Force-Field Hypothesis (EFFH), now formulated as the Theory of Entropicity (ToE). Unlike Einstein’s General Relativity (GR), which attributes perihelion precession to spacetime curvature, we show that it arises naturally from entropy-driven modifications to Newtonian gravity. By introducing higher-order entropy corrections to the gravitational potential of Newton, with inputs from the Unruh Effect, Hawking Temperature, Bekenstein-Hawking Entropy, the Holographic Principle, the Binet Equation, and the Vis-viva Equation, we derive a modified orbital equation that leads to an identical perihelion shift of 43 arcseconds per century, which Einstein derived in 1915 from his momentous General Theory of Relativity (GTR). This result further demonstrates that entropy constraints, rather than curved spacetime, are the fundamental driver of gravitational interactions. Newton’s Classical Theory of Gravitation describes gravity as a force, while Einstein’s General Relativity describes gravity as being as a result of spacetime curvature; but our Theory of Entropicty (ToR) describes gravity as an emergent field from the constraints prescribed by the fundamental Entropic Field.

Obidi shows that Lorentzian spacetime geometry emerges from information geometry via a controlled entropy‑gradient disformal transformation, and that the curvature of this emergent metric reproduces the Einstein gravity of General Relativity (GR). This monograph establishes, with full mathematical and conceptual rigor, the deep structural correspondence between the Obidi Action of the Theory of Entropicity (ToE) and the Einstein–Hilbert Action of General Relativity (GR). We demonstrate that information geometry — comprising the Fisher–Rao metric of classical statistical distinguishability, the Fubini–Study metric of quantum state distinguishability, and the Amari–Čencov α-connections — constitutes the hidden geometric substratum from which gravitational dynamics emerge. The Obidi Action, the variational centerpiece of ToE, accomplishes for the entropic field precisely what the Einstein–Hilbert Action accomplishes for spacetime curvature: it converts a geometric manifold into a dynamical physical arena. We trace the complete logical and mathematical pipeline — from the ontological entropy field S(Λ) through the Hybrid Metric-Affine Space (HMAS), through the α–q constitutive constraint linking Rényi–Tsallis functional deformation to affine geometric asymmetry, and through the emergence of the Master Entropic Equation (MEE) — ultimately recovering Einstein's field equations as the low-gradient, near-equilibrium limit of the entropic field equations. The Einstein–Hilbert Action is thus subsumed within the Obidi Action as a special case, establishing gravity not as a fundamental geometric postulate but as an emergent consequence of information-geometric dynamics. We further examine the Vuli–Ndlela Integral, irreversibility and the arrow of time into the framework. Reviewed landscape of entropic gravity — Jacobson's thermodynamic, Verlinde's gravity, and Bianconi's Gravity.

The Theory of Entropicity (ToE) reconceives entropy not as a statistical by‑product of disorder but as the fundamental field and causal substrate of physical reality. In this framework, entropy 𝑆(𝑥) is elevated to a continuous, dynamical field whose gradients generate motion, gravitation, time, and information flow. The Obidi Action, a variational principle for the entropy field, yields the Master Entropic Equation, Entropic Geodesics, and the Entropy Potential Equation, establishing a unified dynamical foundation. By integrating Fisher–Rao’s classical information metric and the Fubini–Study quantum metric through the Amari–Čencov α‑connection formalism, ToE provides a rigorous geometric and probabilistic structure for physical evolution within an entropic manifold. At its core, the theory reformulates the speed of light as the maximum rate of entropic rearrangement, deriving relativistic and quantum constraints from finite entropy propagation. The No‑Rush Theorem imposes a universal temporal bound on interactions, while the Vuli‑Ndlela Integral, an entropy‑weighted reformulation of Feynman’s path integral, introduces irreversibility and temporal asymmetry into quantum mechanics. Together, these constructs unify thermodynamics, relativity, and quantum theory within a single entropy‑driven continuum. Extending its foundations, ToE incorporates Rényi and Tsallis entropies, establishing a correspondence between generalized entropy measures and geometric structures. The entropic order parameter α emerges as a universal deformation index linking geometry, information, and entropy flow. In this synthesis, ToE reproduces Einstein’s field equations as a limiting case and subsumes Bianconi’s “Gravity from Entropy” as a special instance. Beyond physics, ToE suggests that mass, energy, spacetime, and consciousness arise as emergent constraints of a single entropic reality.

The Theory of Entropicity (ToE) presents a unifying mathematical architecture in which entropy is not a secondary statistical construct but the fundamental field generating all physical geometry, motion, and dynamics. This paper offers both a rigorous and intuitive explanation of how ToE fuses thermodynamics, information geometry, and spacetime physics through the Amari–Čencov α-connections, establishing a coherent field-theoretic foundation. Statistical metrics such as the Fisher–Rao and Fubini–Study are shown to transform into physical metric–affine geometries under entropy-driven deformation governed by the Rényi–Tsallis α–q formalism. Within this framework, entropy acts as an ontological scalar field 𝑆(𝑥,𝑡) S(x,t) whose dynamics are determined by the Obidi Action, yielding the Master Entropic Equation (MEE) as the entropic analogue of Einstein’s field equations. The constitutive relation α = 2(1 – q) mathematically links non-extensive entropy deformation to affine asymmetry, forming the geometric bridge between information flow irreversibility and spacetime curvature. Through this transformation, informational curvature becomes physical curvature, and entropy emerges as the causal fabric that underlies space, time, and matter. Ultimately, the Theory of Entropicity extends Einstein’s geometric paradigm by embedding gravity, quantum mechanics, and thermodynamics within a single entropic continuum. It provides a comprehensive and elegant field-theoretic structure that interprets the universe as an entropy-governed system, where all physical laws, geometries, and interactions arise naturally from the irreversible flow and curvature of the entropic field itself.

The Theory of Entropicity (ToE) unifies Thermodynamics, Quantum mechanics, and General relativity under a single entropic variational principle. This paper reformulates the transformational framework of the ∆∞O meta-theory of Alexander Ngu and Amaya Odilon Kosso through the ToE formalism. Using the Obidi Action and the Vuli-Ndlela Integral, the analysis demonstrates that all transformation-based results claimed by the ∆∞O paper emerge naturally as entropic conse quences. The equivalence transformation program (T1–T6) shows that every major feature—unified operator, Planck-scale dispersion, and holographic entropy bounds—arises from entropic field dy namics governed by irreversible constraints and the finite rate of entropy rearrangement in ToE.