Web App for the Study and Research on the Theory of Entropicity (ToE)

Here is a web supported application for studying and research on The Theory of Entropicity (ToE).

The Theory of Entropicity (ToE)

https://phjob7.github.io/JOO_1PUBLIC/index.html

About the app

I have created a self‑contained educational site that presents the core ideas behind John Onimisi Obidi’s Theory of Entropicity (ToE), highlights its mathematical foundations and key publications, and provides a form where readers can propose extensions to the theory. The app is built using only HTML, CSS and a small amount of client‑side JavaScript, so it runs entirely in your browser—no server or external dependencies are required. It has five main pages:

1. Home – Introduces ToE and explains that it redefines entropy as the fundamental, dynamic field from which spacetime, gravity, motion and even the speed of light emerge.
2. Core Principles – Summarises the theory’s key ideas: entropy as an ontic field, motion and gravity as emergent properties of entropic gradients, time and the speed of light as consequences of entropy flow, and forces as pathways along which entropy redistributes. It also contrasts ToE with Newtonian mechanics and relativity, noting that inertial behaviour and relativistic effects are reinterpreted in entropic terms.
3. Obidi Actions – Explains the Local Obidi Action (LOA) and Spectral Obidi Action (SOA), which together define a variational framework for ToE. The LOA incorporates information‑geometric structures like the Fisher–Rao and Fubini–Study metrics and Amari‑Čencov connections, while the SOA introduces global constraints through spectral data and unifies bosonic and fermionic actions. Their variation yields the Master Entropic Equation governing the evolution of the entropic field.
4. Resources – Lists accessible papers and articles, including the Cambridge preprint deriving Mercury’s perihelion precession from entropic corrections, the Figshare preprint comparing ToE with holographic pseudo‑entropy, the Medium overview that popularises the theory, the official blog explaining the Obidi Actions, and the MDPI encyclopedia entry outlining the theory’s parallels with relativity.
5. Extend ToE – Provides a form that stores user‑submitted titles, ideas and author names in the browser’s local storage and displays them in reverse chronological order. This encourages collaborative exploration and refinement of the theory.

How to use

Download and unzip the application folder. Open index.html in any modern web browser to start exploring. Navigation links allow you to move between sections. To contribute an idea, visit the Extend ToE page, fill in the form and click “Submit Contribution”; your entry will immediately appear below the form.

Application download

You can download the entire web app as a ZIP file here:

https://drive.google.com/drive/folders/1gBnzrQoEEeVKtzDpFm6bpFdms2W2fKX0?usp=sharing

After unzipping, open index.html to use the app offline.

The site and research should give you a solid foundation for understanding and expanding upon the Theory of Entropicity.

Run App Directly From GitHub: The Theory of Entropicity (ToE)

https://phjob7.github.io/JOO_1PUBLIC/index.html

How the Local Obidi Action (LOA) of the Theory of Entropicity (ToE) Reframes Entropy as the Architect of Reality: A New Path in Modern Theoretical Physics

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How the Local Obidi Action Reframes Entropy as the Architect of Reality: A New Path in Theoretical Physics

For more than a century, entropy has remained one of the most misunderstood yet powerful concepts in physics. In thermodynamics it measures disorder, in information theory it measures uncertainty, and in quantum mechanics it encodes the structure of states and entanglement. But in every context, entropy has always played a secondary role—an outcome of physical laws, not their origin.

The Theory of Entropicity (ToE) radically departs from this tradition by placing entropy not at the periphery but at the center of physical law. Its foundational principle is simple yet transformative: entropy is a fundamental field, and its geometry gives rise to the phenomena we call space, time, matter, and gravitation. This conceptual shift leads naturally to a variational framework unlike anything previously attempted—the Local Obidi Action (LOA) and its companion, the Spectral Obidi Action (SOA).

What makes these actions so remarkable is not merely the claim that entropy underlies physical reality, but the mathematical way they accomplish this. For the first time, diverse and seemingly unrelated geometric structures—Fisher–Rao, Fubini–Study, Amari–Čencov α-connections, Tsallis and Rényi entropies, and even Araki’s relative entropy—appear together within a single coherent physical action. This is not a collage of mathematical fragments; it is a unified architecture grounded in the inherent geometry of entropy itself.

Medium readers familiar with general relativity or quantum mechanics may wonder how such disparate tools can coexist inside one theory. The answer lies in understanding what happens the moment entropy becomes a field defined over spacetime rather than a passive numerical descriptor. Once entropy is treated as a fundamental dynamical entity, the geometry that naturally accompanies it is not Riemannian in the traditional sense, but informational. Variations of entropy are variations of distinguishability, coherence, and statistical structure, and these are precisely the objects measured by Fisher–Rao and Fubini–Study metrics. Likewise, the asymmetry and irreversibility of entropy flow are captured by the Amari α-connections. These structures were never designed for gravitational theories because the communities that developed them were not attempting to describe gravity. Yet when ToE reinterprets entropy as the foundational physical field, these tools reveal themselves as the natural geometric language for its dynamics.

This is the conceptual engine behind the Local Obidi Action. The LOA does not bolt together unrelated geometries; it elevates the full informational geometry of entropy into the role traditionally played by spacetime geometry. In this new picture, the entropic metric becomes the stage on which physics unfolds. In some limits it reduces to Fisher–Rao, where classical uncertainties dominate; in quantum-coherent regimes it aligns with Fubini–Study; and across irreversible processes it carries the dualistic imprint of Amari’s α-connections. Generalized entropies—Tsallis, Rényi, and even Araki’s modular entropy—appear as different deformations of this composite entropic geometry. Instead of competing definitions of entropy, ToE unifies them as different aspects of the same underlying field.

What makes this construction even more striking is that no previous program in physics has attempted anything similar. Researchers working in emergent gravity frameworks typically treat entropy as a thermodynamic constraint that reacts to geometry, not a field that generates it. Mathematicians in information geometry rarely venture into gravitational or field-theoretic territory. Quantum information theorists study Fubini–Study geometry and modular operators without interpreting them as candidates for physical curvature. In every case, the work is rigorous, but the motivation remains either statistical or quantum-informational, not cosmological or gravitational.

ToE breaks this boundary by drawing together ideas that previously lived in separate intellectual universes. The unification does not arise from mathematical novelty—Fisher–Rao and Fubini–Study metrics are decades old—but from a new physical principle: entropy is not an emergent descriptor; it is the foundational substance of the universe. Once this principle is adopted, the Local Obidi Action becomes a natural consequence rather than an eclectic choice.

The Spectral Obidi Action pushes this idea even further by translating Araki’s relative entropy—a concept previously confined to the realm of operator algebras and quantum information—into a global variational principle. ToE is the first known theoretical framework to treat Araki entropy not as a diagnostic quantity but as a generator of physical dynamics. This marks a conceptual turning point. It means that modular operators, spectral data, and the deep structure of quantum information become active participants in shaping spacetime and its evolution. The SOA introduces non-local and global constraints that complement the local differential structure of the LOA, forming a two-tier variational architecture unparalleled in the current literature.

The originality of the Obidi Actions comes not from inventing new mathematical objects but from understanding that existing structures gain profound physical meaning when entropy is recognized as the principal field of nature. From this vantage point, the diversity of generalized entropies is not a theoretical nuisance but a reflection of entropy’s multidimensional geometric character. The richness of information geometry is not a mathematical curiosity but the true geometric signature of the universal entropic field.

For the first time, these elements—classical and quantum, reversible and irreversible, local and spectral—find their place within a single unified theory. The Local Obidi Action becomes the differential engine of entropic dynamics, while the Spectral Obidi Action becomes the global regulator of consistency across the entire entropic manifold. Together, they outline a new foundation for physics in which entropy does not merely measure the state of the universe but constructs it.

If the history of physics teaches anything, it is that conceptual breakthroughs often happen when familiar ideas are reinterpreted under new principles. Just as Einstein reimagined spacetime through the lens of relativity, and Feynman reimagined quantum behavior through path integrals, ToE offers a reimagining of entropy as the architect of reality. Whether this framework becomes a cornerstone of future theoretical physics remains to be seen, but its conceptual depth and mathematical boldness mark it as one of the most intriguing developments of the modern era.

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How Obidi’s Local Obidi Action (LOA) Is Able to Incorporate Generalized Entropies and Multiple Information-Geometric Structures

 

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(1) How Obidi’s Local Obidi Action (LOA) Is Able to Incorporate Generalized Entropies and Multiple Information-Geometric Structures

The Local Obidi Action (LOA) achieves something unusual in contemporary theoretical physics: it brings together a family of mathematical structures—generalized entropies, Fisher–Rao geometry, Fubini–Study geometry, and the Amari–Čencov α-connections—within a single variational field framework. At first glance this seems astonishing, as these formalisms typically live in different mathematical and disciplinary worlds. Yet the synthesis emerges naturally once entropy is elevated to the status of a fundamental physical field.

The conceptual pivot of ToE is the decision to treat the entropy field as something far deeper than a thermodynamic bookkeeping quantity. In the ToE perspective, entropy becomes the organizing field from which geometry, dynamics, and even perceptible physical laws emerge. Once this shift is made, the question becomes unavoidable: if entropy is a fundamental field, what is its natural geometry? The answer does not come from classical differential geometry but from the mature mathematical theory of information geometry, a body of knowledge developed over several decades by pioneers such as Čencov, Amari, Nagaoka, Petz, and others.

Information geometry already knows how to measure variation of entropy: the Fisher–Rao metric expresses infinitesimal statistical distinguishability, the Fubini–Study metric captures the geometry of quantum states, and the Amari α-connections describe the dualistic affine structures that underlie entropy production and irreversibility. These are not arbitrary mathematical decorations; they are the canonical ways of measuring and differentiating entropy-related structures. Once the entropy field becomes fundamental, these metrics and connections become natural candidates for the very geometry that the field “lives on.”

The LOA unifies these structures by relying on a simple but powerful observation: the entropy field is simultaneously a classical statistical object, a quantum informational object, and a thermodynamic object. Each of these aspects comes with its own intrinsic geometry, and the entropic metric constructed within LOA is designed to carry all of these geometric signatures at once. In the appropriate limits, the entropic metric reduces to the Fisher–Rao form, while in the quantum-coherent regime it reduces to the Fubini–Study sector. The Amari α-connections appear automatically as the affine structure compatible with the entropy-dependent metric. Tsallis, Rényi, and Araki–Umegaki entropies enter through the deformation of the metric and through the spectral components of the theory.

What makes this synthesis coherent rather than chaotic is the logic that underpins it: if entropy is the foundational field of physics, its geometry must reflect all of the informational, statistical, and quantum structures that entropy already carries. The LOA is therefore not a random combination of unrelated mathematical constructions but a principled elevation of entropy’s full geometric content into the language of field theory and gravitation. Seen in this light, the incorporation of multiple entropies and information-geometric formalisms is not an accident or an embellishment; it is the necessary mathematical expression of entropy’s intrinsic structural richness.

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(2) Why No Other Researcher Has Attempted This Synthesis Before

Although the mathematical ingredients of the Theory of Entropicity (ToE) are well-known individually, the specific synthesis achieved in the Local Obidi Action and its pairing with the Spectral Obidi Action is unprecedented in the scientific literature. The reason is not simply that earlier researchers lacked imagination; rather, their starting assumptions, disciplinary traditions, and methodological constraints positioned them far from the unification that ToE naturally leads to.

Historically, entropy in physics has played a derivative or diagnostic role. In relativity, black-hole thermodynamics, or Jacobson-type emergent gravity theories, entropy is treated as something that arises from geometry or matter fields, not something that generates them. These approaches view entropy as a constraint or an emergent quantity, not a fundamental dynamical variable. Because of this, their mathematical formulations do not require the full machinery of information geometry, nor do they attempt to build an action in which entropy is the primary field.

A completely different intellectual tradition developed in statistics, probability theory, and quantum information science. There, researchers studied Fisher–Rao geometry, Fubini–Study geometry, and the Amari–Čencov α-connections purely as mathematical structures characterizing statistical models or quantum states. These works were not aimed at constructing physical field theories, let alone gravitational theories. As a result, the mathematical tools remained confined to abstract manifolds of probability distributions or Hilbert-space projective geometries. The idea that these geometries might serve as the foundational geometry of spacetime itself would have required a conceptual leap that fell outside the aims of those communities.

A third technical barrier concerned the use of generalized entropies—such as Rényi, Tsallis, and especially Araki relative entropy—in dynamical variational principles. These entropies appear widely in information theory, quantum computation, machine learning, and statistical mechanics. Yet they are very rarely embedded inside an action functional, and essentially never in a gravitational action. In all known literature, Araki’s relative entropy is used as a diagnostic quantity in operator algebras or in modular theory, not as a Lagrangian that can be varied to produce field equations. This historical pattern made it unlikely that someone working within conventional academic pathways would ever attempt to promote such entropies to dynamical status.

The Theory of Entropicity breaks with this tradition by taking seriously the proposition that entropy is not an emergent measure but a fundamental field whose variations generate the physical laws of the universe. Once this assumption is made, the use of generalized entropies becomes natural, and the mathematical tools of information geometry become indispensable. The LOA becomes the natural home for these structures, and the SOA becomes the natural global constraint, much as the Einstein–Hilbert action became the natural home for curvature as soon as Einstein accepted that gravity was geometry.

In this sense, the originality of the Obidi framework lies not in the invention of new mathematical objects but in recognizing that entropy’s full informational geometry can and should be elevated to the status of physical geometry. No established research program has done this because no prior program has begun from the same first principles. The synthesis achieved in ToE required stepping outside traditional silos and unifying three domains—gravity, information geometry, and generalized entropy—in a way that each of them alone had never suggested. It is precisely this willingness to treat entropy as a universal field that permits the Local Obidi Action to express so many previously unrelated structures in a single, coherent mathematical form.

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On the Two Action Principles of the Theory of Entropicity (ToE): The Local Obidi Action (LOA) and the Spectral Obidi Action (SOA)

On the Two Action Principles of the Theory of Entropicity (ToE): The Local Obidi Action (LOA) and the Spectral Obidi Action (SOA)

The Theory of Entropicity (ToE), proposed by John Onimisi Obidi, defines the dynamics of the universe through two primary variational principles, referred to as the Obidi Actions. 

These two "Actions" are:

• The Local Obidi Action (LOA): This is the geometric sector of ToE, which integrates curvature, asymmetric transport, and entropy gradients into a single variational principle. It describes the differential dynamics of the entropy field at local points in spacetime and is analogous to the Einstein–Hilbert action in General Relativity, from which the Master Entropic Equation (MEE) is derived.
• The Spectral Obidi Action (SOA): This action provides a global formulation of the physics through operator traces, introducing a Dirac-type entropy operator. The spectrum of this operator regulates coherence, scale, and regularity, encoding quantum features directly into the mathematical framework and bridging the gap between local field equations and global consistency. 

Together, these two actions ensure that geometry, entropy, and quantum properties are intrinsically coupled and interdependent, forming a unified, self-consistent framework where entropy is the fundamental field of reality. 

Obidi's First and Second Heresies in the Theory of Entropicity (ToE) of Modern Theoretical Physics

Obidi's First and Second Heresies in the Theory of Entropicity (ToE) of Modern Theoretical Physics 

"Obidi's Heresy" is a concept within John Onimisi Obidi's Theory of Entropicity (ToE) that refers to the radical claim of dethroning the observer from its central, privileged role in modern theoretical physics, particularly in quantum mechanics and relativity.

Obidi's dethronement of the Observer is actually Obidi's Second Heresy.

Obidi's First Heresy consists in his primary declaration of Entropy as a field rather than just a 

statistical or quantitative measure of disorder or ignorance or uncertainty.

Explanation of Obidi's Heresy

In many interpretations of physics, such as the Copenhagen interpretation of quantum mechanics or the observer-dependent frames of reference in Einstein's relativity, the observer plays a crucial role in defining reality or measurement outcomes. Obidi's Second Heresy challenges this anthropocentric view. 

Key aspects of the "heresy" include:

• Observer Marginalized: Obidi argues that observers are merely local subsystems embedded within the universal entropic field and are constrained by its dynamics, rather than standing outside as independent arbiters of reality.
• Entropy as Primary: Reality is not participatory or observer-created; instead, it is "pre-computed" and governed by the autonomous, dynamic entropic field, which exists independently of human observation.
• Objective Reality: This stance reasserts a form of objective reality, where physical laws and phenomena are consequences of entropy's dynamics, not the observer's frame of reference or act of measurement. 

Essentially, Obidi's First Heresy is the bold and radical assertion that the universe's fundamental architecture is determined by entropy as a universal field, rendering the observer's role secondary and non-privileged in the grand scheme of physical reality — which is Obidi's Second Heresy (the Observer Dethroned!). The theory itself is a recent, non-mainstream proposal still undergoing rigorous mathematical development and conceptual refinements to gain wider and universal acceptance in the scientific community.  

Conclusion 

Within the context of the ToE, these "heresies" refer to fundamental challenges the theory poses to established physics principles: 

• Obidi's First Heresy (against established physics): This refers to the core postulate that entropy is the fundamental, causal field of physical reality, rather than a mere statistical byproduct or measure of disorder. Traditional physics treats entropy as an emergent property of underlying dynamics; ToE inverts this, making entropy primary and all other phenomena (spacetime, gravity, motion, quantum mechanics) emergent from it.
• Obidi's Second Heresy (against the role of the observer): This relates to the assertion that the observer is "dethroned" from a privileged or central role in physics. In ToE, reality and physical processes (like quantum wave function collapse or the structure of spacetime) are governed by the objective, dynamic entropic field, independent of observation or measurement. The observer is considered an embedded, local subsystem constrained by these entropic dynamics, challenging interpretations in quantum mechanics (like the Copenhagen interpretation) and relativity that place the observer's frame of reference as central. 

These concepts are part of an ongoing development of the Theory of Entropicity (ToE), primarily discussed in papers and articles authored by Obidi and published on platforms like Medium, Substack, ResearchGate, and Figshare, CoE, SSRN, International Journal of Current Science Research and Review (IJCSRR), Authorea, OSF, etc.

On the Heretical Foundation and Yet Logical and Mathematical Consistency of the Theory of Entropicity (ToE) in Modern Theoretical Physics: Obidi's Heresy! 

In the Theory of Entropicity (ToE), John Onimisi Obidi has been able to invent the Local Obidi Action (LOA) and incorporated such diverse components like generalized entropies of Rényi and Tsallis, the information geometry of Fisher-Rao and Fubini-Study metrics, and  the Amari-Čencov alpha connections. After inventing this local action, Obidi went on further to develop the Spectral Obidi Action (SOA), thus incorporating spectral operator formalism into the Theory of Entropicity ToE as an overarching Action that subtly incorporates the Araki Relative Entropy and Spectral Geometry. 

As far as we know based on all current literature accessible to us, no other researcher and investigator has attempted such a generalization and feat of unification.

Thus, what John Onimisi Obidi has achieved is unusual; and—in the literal, technical sense—nobody else has built a single local variational action that explicitly weaves together:

• generalized entropies (Tsallis, Rényi, Araki, etc.),
• Fisher–Rao, Fubini–Study, and Amari–Čencov geometry,
• and gravity/field dynamics

in the way the Local Obidi Action (LOA) and its pairing with SOA do in ToE. At an initial hasty glance, this rather unusual integration could be deemed heretical. Only after some sorber and humble reflection can one realize that this feat is both original and groundbreaking in the annals of Science.

Let us now investigate how Obidi has managed to do it, and why the literature hasn’t gone there before Obidi did.

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1. What the Local Obidi Action actually is, structurally

If you strip away the Entropicity branding and look at the bare structure, the LOA is essentially built from three intertwined pieces:

1. A scalar field sector – the entropy field with a kinetic term and a potential.
2. A geometric sector – a metric (or metric family) that is not just the spacetime metric , but an entropic metric that already carries Fisher–Rao / Fubini–Study / Amari structure.
3. A coupling to gravity – Ricci scalar and curvature built from the entropically deformed metric.

So instead of:

• “Here is a scalar field + GR as two separate things,”

Obidi declares that:

• “The scalar field is entropy,
• and its geometry is information geometry,
• and its coupling to curvature is gravity.”

Once we accept that axiom, it becomes natural (for us) to pull in Fisher–Rao, Fubini–Study, and Amari–Čencov, because in accordance to Obidi's mental picture:

“Wherever there is entropy, there is an information metric; wherever there is an information metric, there is geometry; wherever there is geometry, there can be a variational action.”

Most people in the literature stop at one of those arrows and never compose all three [in the way Obidi has done].

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2. Why LOA can host Fisher–Rao, Fubini–Study and Amari–Čencov at once

There are three existing “worlds” that Obidi noticed all share the same backbone:

• Fisher–Rao – the metric on probability distributions (classical information geometry).
• Fubini–Study – the metric on pure quantum states (projective Hilbert space).
• Amari–Čencov α–connections – the family of affine connections that live on statistical manifolds, encoding duality and irreversibility.

In mainstream [physics] work, these are usually treated as:

• mathematical curiosities in statistics or quantum foundations,
• tools for machine learning or information geometry,
• or at most, hints about “information in gravity.”

But Obidi did something slightly heretical but logically and mathematically clean — Obidi boldly declares:

1. Promote entropy from a number to a field .
2. Promote its information geometry to the actual physical geometry of the “entropic manifold.”
3. Explicitly choose Fisher–Rao + Fubini–Study + Amari α–connections as the components of that geometry, and then
4. Feed that composite geometry directly into an action principle (LOA) that also talks to gravity.

So, the Local Obidi Action (LOA) is not “randomly mixing” things; it is taking seriously the idea that:

“The right geometry for an entropy field is information geometry, and the right language for dynamics on a geometry is a variational action.”

Once we write down that action, all three structures appear almost inevitably. 

This is Obidi's [First] Heresy!

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3. Why no one else has done exactly this (so far)

There are several historical and sociological reasons for this, not just “they missed it”:

a) Different starting questions

• Jacobson, Padmanabhan, Verlinde:
  They started from: “Can gravity be derived from thermodynamics?”
  So entropy is a constraint or diagnostic on an already-existing spacetime; the metric is primary.

• Amari, Čencov, information geometers:
  They started from: “What is the natural geometry of probability distributions?”
  Gravity and spacetime are not their target; physics is at best a side application.

• Quantum geometers (Fubini–Study, Bures, etc.):
  They started from: “What is the geometry of quantum state space?”
  Again: no attempt to build a full gravitational field theory from it.

But, again, Obidi started from a very different question:

“What if entropy is the fundamental field of nature, and its information geometry is the geometry that all physics lives on?”

Once we ask that question and insist on a true field theory, the Local Obidi Action (LOA) becomes the natural language to express it.

b) Disciplinary silos

The people who deeply understand:

• Araki entropy and modular operators,
• spectral geometry and Connes–Chamseddine actions,
• Fisher–Rao / Amari α–connections,
• Fubini–Study in QFT/QI,
• and entropic gravity

are usually not the same person or even in the same research community.

Obidi's work is thus unusual because we see that Obidi has indeed:

• studied entropic gravity (Verlinde, Bianconi, Jacobson),
• studied information geometry (Amari–Nagaoka, Čencov),
• studied quantum geometry and spectral stuff,
• and then refused to treat them as separate hobbies or disciplines.

That cross-silo synthesis is rare—even more so for someone working independently.

c) Risk profile

It is much safer in academia to:

• add a small correction to GR,
• or apply Fisher–Rao to machine learning,
• or talk about “entropic gravity” near black holes,

than to say:

“I am writing a new action principle where entropy is the fundamental field and all of Fisher–Rao, Fubini–Study, Amari α, Tsallis, Rényi, and Araki are unified as one geometric-variational structure.”

That sounds “too big” and will scare most grant reviewers. But Obidi has not been constrained by that incentive structure, so Obidi can afford to be bold.

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4. Is it really true that no one has done what Obidi has done?

We are able to note the following in an objective fashion:

• There are works that connect Fisher information and gravity;
• there are works that connect entropy and gravity (Verlinde, Bianconi, etc.);
• there are works that connect Fisher–Rao and Fubini–Study;

But:

• We do not find any pre–ToE work in which a single local variational action:
  • takes an entropy field as fundamental,
  • uses information geometry (Fisher–Rao, Fubini–Study, Amari α) as its metric content, and
  • couples that to gravity as the dynamical backbone for all of physics.

The only place that precise combination appears is in Obidi's own Theory of Entropicity (ToE) papers, blog, and encyclopedia entry.

So, we can state as follows:

The ingredients existed in the literature, but the specific synthesis and the Local Obidi Action as a unifying entropic action are original to ToE, as far as current published research shows.

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5. Closure on Obidi's originality 

What John Onimisi Obidi has done is not:

• invent Fisher–Rao,
• invent Fubini–Study,
• invent Amari α–connections,
• or invent entropy itself.

What is new is Obidi's conceptual foundation and integration:

• treating entropy as a field,
• insisting that its natural geometry is information geometry,
• lifting that geometry directly into a gravitationally coupled action,
• and then using that as the backbone of a unified theory (ToE).

This is Obidi's First Heresy!

That kind of “conceptual recombination” is where a lot of real originality lives in theoretical physics. 

Einstein did not invent Riemannian geometry; he saw what it meant physically. John Onimisi Obidi has therefore done something similar at the level of entropy + information geometry + gravity.

The Theory of Entropicity (ToE) App: Homepage of the Theory of Entropicity (ToE) App - https://replit.com/@jonimisiobidi/Entropy-Weaver

 The Theory of Entropicity (ToE) App

Entropy Weaver - Replit

https://replit.com/@jonimisiobidi/Entropy-Weaver

Here is an interactive web application for exploring and understanding the Theory of Entropicity (ToE) with visualization tools, mathematical frameworks, and collaborative research features

The Theory of Entropicity (ToE) application includes the following features:

1.) Interactive concept explorer with hierarchical visualization of ToE's core concepts (entropy as fundamental field, emergent gravity, ETL, speed of light reinterpretation)

2.) Mathematical framework viewer displaying key equations (Obidi Action, Master Entropic Equation,

3.) Vuli-Ndlela Integral) with LaTeX rendering and interactive parameters

4.) Visual entropy field simulator showing 2D/3D representations of the entropic field S(x,t) with adjustable parameters

5.) Comparative analysis tool to explore relationships between ToE and other theories (General Relativity,

Quantum Mechanics, Verlinde's entropic gravity)

6.) Research notebook feature for documenting insights, hypotheses, and extensions with rich text editing and equation support

7.) Knowledge base with comprehensive ToE documentation, key papers, and concept definitions organized by topic

8.) Clean, academic interface with dark mode option, professional typography optimized for reading complex physics content

Homepage of the Theory of Entropicity (ToE) App

Comparison Between the Theory of Entropicity (ToE) and Einstein's General Relativity (GR)

Theory of Entropicity

General Relativity

Aspect	Theory of Entropicity	General Relativity
Fundamental Entity	Entropy field S(x,t)	Spacetime metric g_μν
Gravity Source	Entropy gradients	Mass-energy curvature
Speed of Light	Maximum entropy reorganization rate	Postulated constant
Time	Emergent from entropy dynamics	Coordinate in spacetime manifold
Field Equations	Master Entropic Equation	Einstein Field Equations
Variational Principle	Obidi Action	Einstein-Hilbert Action
Mercury Precession	Entropy corrections	Spacetime curvature

Understanding the Comparison

Key Differences

ToE fundamentally differs from traditional physics by treating entropy as the primary ontological entity. While other theories treat spacetime, fields, or particles as fundamental, ToE proposes that these all emerge from the entropic field.

Unification Approach

Rather than trying to quantize gravity or geometrize quantum mechanics, ToE takes a third path: deriving both from a single entropic principle. This is analogous to how thermodynamics unified heat and mechanics.

Understanding the Comparison

Key Differences

ToE fundamentally differs from traditional physics by treating entropy as the primary ontological entity. While other theories treat spacetime, fields, or particles as fundamental, ToE proposes that these all emerge from the entropic field.

Unification Approach

Rather than trying to quantize gravity or geometrize quantum mechanics, ToE takes a third path: deriving both from a single entropic principle. This is analogous to how thermodynamics unified heat and mechanics.