Theory of Entropicity (ToE) by John Onimisi Obidi: Concept of the Obidi Curvature Invariant (OCI) in the Theory of Entropicity (ToE): Concise Notes on Applications and Derivations

Thursday, 29 January 2026

Concept of the Obidi Curvature Invariant (OCI) in the Theory of Entropicity (ToE): Concise Notes on Applications and Derivations

The Obidi Curvature Invariant (OCI) is a concept introduced in the Theory of Entropicity (ToE), a theoretical framework developed by physicist John Onimisi Obidi. In this theory, entropy is reinterpreted not merely as a statistical measure of disorder but as a fundamental physical field that permeates spacetime, from which other phenomena like gravity, quantum mechanics, and information processing emerge.

At its core, the OCI is defined as the natural logarithm of 2 (ln 2 ≈ 0.693), elevated to the status of a universal geometric constant. It represents the smallest nonzero curvature divergence or deformation in the entropic field that the universe can recognize as a distinct informational state or configuration. This makes it the fundamental "quantum of distinguishability"—the minimal threshold for two states to be physically separable or observable as different. In essence, OCI acts as the universe's resolution limit for entropic changes, analogous to how Planck's constant sets a scale in quantum mechanics, but here tied to information and curvature in an entropic manifold.

Key Aspects in the Theory of Entropicity:

Geometric Role: OCI emerges from the geometry of the entropic field, where information corresponds to localized curvature. The value ln 2 is derived as the smallest nontrivial deformation capable of supporting two distinct states (e.g., like distinguishing between a "0" and "1" in binary information at the most fundamental level).

Entropic Cost and Dynamics: It serves as the basic unit of entropic "cost" in processes involving information reconfiguration. For instance, quantum transitions or state distinctions occur only when the entropic curvature crosses multiples of this invariant.

Applications and Derivations: Obidi uses OCI to derive established principles from first principles, such as Landauer's Principle (the minimum energy cost of erasing information, k_B T ln 2) and the Landauer-Bennett cost in computing. It also plays a role in unifying gravity and quantum effects, for example, by linking to the Einstein Field Equations or Schrödinger's equation through the Spectral Obidi Action (SOA)— (a variational principle in ToE).

ToE, including OCI, is a radical and audacious proposal that challenges mainstream physics by positing entropy as the primary substrate of reality, with spacetime emerging from it. While it draws on established constants like ln 2 from information theory and thermodynamics, it is still being vigorously researched and developed for wider acceptance in the scientific community. It appears primarily in Obidi's publications on platforms like Medium, Substack, ResearchGate, Figshare, International Journals like (IJCSRR), Cambridge University COE, SSRN, Academia, and LinkedIn, among other channels. For deeper exploration and insights, reviewing Obidi's derivations (e.g., involving the Master Entropic Equation or entropic holography) is highly recommended to the curious and serious reader.