The Redemption of the Theory of Entropicity (ToE): On the Logical Trajectory to "Why Entropy Must be a Field"—The Conceptual Loop of ToE
In my development of the Theory of Entropicity (ToE), I have elevated entropy to the status of a field based on a series of logical arguments: from Entropy to information/uncertainty to geometry to field and then field back to entropy.
In achieving the above conceptual loop for the Theory of Entropicity (ToE), I have, in effect, closed the loop: starting from entropy as a statistical/informational quantity, I push it through information geometry into spacetime geometry, promote that geometric structure to a field, and then re-interpret that field as entropy again.[1][2][3] That circular passage is exactly what makes “entropy as a field” non-hand‑wavy in your ToE, rather than a mere slogan.
The logical chain I have used in my invention of ToE
Very schematically, what I have built (and what the ToE papers already hint at) is:
1. Entropy → information
We begin by having to take thermodynamic and generalized entropies (Boltzmann–Gibbs, Rényi, Tsallis) as measures on probability distributions, i.e., on information states.[1][4] These quantify distinguishable micro-configurations and their deformations via parameters like $$q$$ or $$\alpha$$.
2. Information → geometry
I then went on to put these distributions on a statistical manifold with Fisher–Rao / Amari–Čencov structure, so that entropy and its deformations induce a Riemannian or metric–affine geometry on that manifold.[3][4] In this language, entropy gradients, divergences, and flows become geometric objects (connections, curvatures, geodesics) on the space of states.
3. Geometry → field
Next, I externalize that information geometry onto physical spacetime: the same entropy-induced metric–affine structure is reinterpreted as a field $$S(x,t)$$ with associated geometric data (metric, connection) living on spacetime itself.[1][3] This is where the Obidi Action and Master Entropic Equation (MEE) enter as the field equations for that entropic geometry, analogous to Einstein’s equations for $$g_{\mu\nu}$$.[3][5]
4. Field → entropy (closing the loop)
Finally, I go on to demand that this spacetime field and its geometry are not “something else” that entropy happens to influence, but are entropy in field form: spacetime curvature, inertial motion, and even quantum behavior are interpreted as manifestations of the dynamics of the entropic field and its gradients.[1][2][3] In that sense, the field is not merely sourced by entropy; it is entropy, written in geometric variables.
Why this rescues “entropy is a field” in ToE
In standard physics, promoting entropy to a field is conceptually shaky unless one says what the field is a field of (which microstates, which ensemble, which coarse-graining, etc.).[6][7] My ToE chain (conceptual loop) is an explicit answer to that objection:
- The domain of the field is spacetime, but its origin is a statistical manifold of configurations, equipped with an information metric derived from entropy.[3][4]
- The dynamics of the field are not arbitrary; they come from a variational principle (Obidi Action) that encodes how entropy deformations (through $$\alpha,q$$, etc.) curve the information geometry and, via my ToE identification, physical spacetime.[3]
- The interpretation of the field remains entropic because every geometric object in the theory (metric, connection, curvature) traces back to an entropy (or information) functional on an underlying space of possibilities.[1][2][3]
So, when I posit that “entropy is a field” in the Theory of Entropicity (ToE), I am not reifying a bare scalar; rather, I am pointing to a specific geometric structure whose very definition is built from entropy and information, and whose dynamics send us back to entropic evolution. The conceptual crossroads I identified for ToE—where naïvely calling entropy a field makes it unintelligible—is exactly where the ToE entropy → information/uncertainty → geometry → field → entropy loop is doing its hardest and most important work.
Citations:
[1] John Onimisi Obidi - Independent Researcher https://independent.academia.edu/JOHNOBIDI
[2] (PDF) Collected Works on the Theory of Entropicity (ToE) Volume I 31 ... https://www.academia.edu/145698037/Collected_Works_on_the_Theory_of_Entropicity_ToE_Volume_I_31_December_2025_V9_S
[3] A Simple Explanation of the Unifying Mathematical Architecture of ... https://client.prod.orp.cambridge.org/engage/coe/article-details/68f6f7abaec32c6568313403
[4] A new class of entropic information measures, formal group theory ... https://pmc.ncbi.nlm.nih.gov/articles/PMC6405454/
[5] Transformational Unification through the Theory of Entropicity (ToE) https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/68f6f66c5dd091524f8f362e/original/transformational-unification-through-the-theory-of-entropicity-to-ea-reformulation-of-quantum-gravitational-correspondence-via-the-obidi-action-and-the-vuli-ndlela-integral.pdf
[6] Entropy Density - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/computer-science/entropy-density
[7] Entropy in thermodynamics and information theory - Wikipedia https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory
[8] Unified framework for the entropy production and the stochastic interaction based on information geometry https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.2.033048
[9] Entropic theory of Gravitation https://www.academia.edu/33008874/Entropic_theory_of_Gravitation
[10] Spherically symmetric black holes in Gravity from Entropy and spontaneous emission https://www.arxiv.org/pdf/2602.13694.pdf
[11] On the Conceptual and Mathematical Foundations of the ... - Wiley https://wiley.authorea.com/users/896400/articles/1346238-on-the-conceptual-and-mathematical-foundations-of-the-theory-of-entropicity-toe-an-alternative-path-toward-quantum-gravity-and-the-unification-of-physics
[12] Study Suggests Quantum Entanglement May Rewrite the Rules of ... https://thequantuminsider.com/2025/05/11/study-suggests-quantum-entanglement-may-rewrite-the-rules-of-gravity/
Also refer to the earlier directly related work:
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