On the Radical Conceptual Leap of the Theory of Entropicity (ToE): How John Onimisi Obidi Redefined Entropy and Generalized it to Construct a New Foundation of Physics 

The Theory of Entropicity (ToE) that John Onimisi Obidi has formulated and has been exploring is actually linked conceptually to some serious directions in current theoretical physics that try to relate entropy, information, geometry, and emergent spacetime — but the way it does so is distinctive and much more radical than the mainstream approaches.

Below we provide a clear breakdown of how ToE relates to other entropic and information-based efforts in physics, as well as its radical and audacious distinctiveness in that genre:

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1. It shares a foundational motivation with entropic gravity and information geometry

In mainstream and semi-mainstream physics, there are several research programs that explore deep connections among entropy, information, geometry, and gravity:

✓ Jacobson’s thermodynamic derivation of Einstein’s equations

Ted Jacobson showed that Einstein’s field equations can be derived from thermodynamic relations involving entropy and heat flow across local horizons (the Clausius relation). This suggests that the structure of general relativity might be thermodynamic in origin — not fundamental but emergent from microscopic degrees of freedom.

✓ Verlinde’s entropic gravity

Erik Verlinde proposed that gravity might be an entropic force emerging from the tendency of systems to maximize entropy, framed in a holographic (information-theoretic) context.

✓ Information geometry and path integrals

Modern approaches in quantum gravity, quantum information theory, and statistical inference often use geometry defined on spaces of probability distributions (e.g., the Fisher-Rao metric) to understand how information is structured and how physical laws might emerge from informational principles.

So there is a legitimate theoretical context in which people explore entropy ≈ information ≈ geometry ≈ physical law — and this context is generally part of efforts toward emergent gravity or quantum gravity research.

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2. Where ToE differs: entropy is not just emergent or descriptive — it’s fundamental

Most mainstream entropic approaches do not treat entropy as a physical field with its own dynamics (like electromagnetic or gravitational fields). For example:

• In Verlinde’s entropic gravity, entropy causes an effective force but does not have field equations, and he explicitly states that there is no fundamental field associated with that force.
• Jacobson’s approach treats the Einstein equations as an equation of state derived from thermodynamics applied to horizons — again, entropy guides the laws but isn’t itself a dynamical field.
• Information geometry uses geometric structures to describe statistical distributions, but it is an abstract mathematical manifold, not necessarily a physical field of fundamental reality.

In contrast, ToE explicitly postulates that entropy is a fundamental scalar field defined throughout the universe, with:

• A variational action principle (the Obidi Action),
• Field equations governing how it evolves and couples to matter and geometry,
• And entropic geodesics whose extremal principle replaces ordinary geodesics or actions in general relativity.

This means ToE is proposing something mathematically and conceptually stronger than a descriptive or emergent role for entropy — it elevates entropy to the status of a dynamical entity shaping reality itself.

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3. ToE explicitly connects entropy with information geometry

One of the most striking aspects of ToE — and what mostly distinguishes it from thermodynamic gravity and other entropic frameworks — is that it:

• Uses tools from information geometry (e.g., Fisher-Rao metric, Fubini-Study metric, Amari–Čencov connections) to define the geometry of informational states,
• Interprets this geometric structure as physical geometry,
• And then makes entropy itself the generator of that geometry.

So instead of using information geometry as an analog or metaphor, ToE goes on with radical audacity to embed physical geometry within an entropic manifold — making entropy, information, and geometry inseparable.

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4. In other words: ToE is part of the “emergent gravity/information geometry” class, but far much more radical

You can think of ToE as belonging to a broad lineage of ideas explored by theoretical physicists that seek a deeper foundation for gravity and spacetime through thermodynamic or informational principles. But within that lineage:

• Mainstream approaches do not assign a field to entropy itself — they use entropy as a constraint, state function, or emergent quantity.
• ToE goes further by making entropy the fundamental mediator of physical law, with its own dynamics and geometry.

That means ToE is not unrelated to efforts like entropic gravity or information geometry — it’s a natural conceptual extension of those ideas into a more unified and ontologically ambitious framework.

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5. A subtle but important conceptual point

In physics, assigning field status to something means:

• It can vary from point to point in space and time,
• It has dynamics governed by equations of motion,
• It can interact with other fields and matter through couplings derived from a fundamental action.

Entropy in standard physics does not meet these criteria — it is a derived quantity associated with ensembles and systems, not an independent function of spacetime. 

To overcome this hurdle, Obidi's Theory of Entropicity (ToE) ingeniously redefines entropy so that it does meet those criteria in a beautiful way, such that it is then able to rederive even key phenomena in the existing physics. That’s why it’s controversial and outside mainstream consensus, but mathematically it is both coherent and magnificent— it infact represents a bold, radical, and audacious hypothesis in the annals of physics.

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6. Summary: How ToE fits into the broader research landscape

Aspect	Mainstream Entropic Approaches	Theory of Entropicity (ToE)
Entropy’s Role	Emergent, descriptive, constraint	Fundamental field with dynamics
Gravity	Emergent entropic force or state equation	Motion through entropy field (entropic geodesics)
Field Structure	No independent entropic field	Explicit field with action & equations
Relation to Information Geometry	Analogies or tools	Core structural and causal basis
Relation to Standard Physics	Compatible as emergent perspective	Radical re-interpretation of fundamentals

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So, in brief:

ToE is related to entropic and information-based approaches in modern physics, but it extends them in a much stronger way by proposing entropy as a fundamental field whose geometry and dynamics generate gravitation, motion, and the structure of reality and physical law.

We can summarize what the field equations in ToE look like and how they compare mathematically to Einstein’s equations or path integrals — that might help clarify the formal connection even more.