Beyond Comparison: Why the Theory of Entropicity (ToE) Reconstructs Reality from Entropy

Beyond Comparison: Why the Theory of Entropicity (ToE) Reconstructs Reality from Entropy

Introduction:

Two Roads into Entropy

Entropy has always been a measure—of disorder, of uncertainty, of information. But in recent years, physicists have begun to ask whether entropy might be more than a tool. Could it be the foundation of reality itself?

Two striking approaches have emerged. Ginestra Bianconi’s Gravity from Entropy (2025) reframes gravity as arising from quantum relative entropy between spacetime and matter metrics. John Onimisi Obidi’s Theory of Entropicity (ToE) goes further, proposing that entropy is not a comparison but the field of reality itself.
Both are bold. Both are entropic. But they are not the same.

Bianconi’s Entropic Gravity:

Geometry as Information

In Bianconi’s framework, gravity is derived from the quantum relative entropy between two metrics:

\mathcal{L} = \mathbf{Tr}

- \tilde{G}\, the metric of spacetime

- \tilde{g}\, the metric induced by matter fields

The Bianconi action is then written as:

\mathcal{L} = \mathbf{Tr} \, \tilde{g} \ln \tilde{G}^{-1} = - \mathbf{Tr}_F \ln \tilde{G} \tilde{g}^{-1}

This formulation treats gravity as the entropic mismatch between geometry and matter. By introducing a G-field as a Lagrange multiplier, Bianconi derives modified Einstein equations with a small positive cosmological constant.

Her approach is elegant:

Gravity is not imposed but emerges from information geometry. Entropy becomes the language of spacetime curvature.

ToE’s Entropic Field:

Reality as Entropy

John Onimisi Obidi’s Theory of Entropicity (ToE) takes a more radical stance. It argues that entropy is not a measure of reality—it is reality.

In ToE:

- The Spectral Obidi Action (SOA) reframes Araki relative entropy as a dynamical action principle, not a static measure.

\mathcal{S}_{\mathrm{SOA}} = - \mathrm{Tr} \ln \Delta

- The No-Rush Theorem enforces finite-rate bounds on entropy redistribution, making causality and relativistic effects physical consequences of entropy.

- Length contraction and time dilation are not kinematic artifacts but field-driven realities, enforced by entropy’s constraints.

- Observers are secondary: what they see has already been computed by the entropic field. Relativity itself is emergent.

ToE integrates Shannon, von Neumann, Rényi, Tsallis, KL, and Araki entropies into a unified spectral-geometric framework, coupling them with Fisher–Rao and Fubini–Study metrics via Amari–Čencov connections. It is not just a theory of gravity—it is a theory of everything entropic.

The Crucial Difference

The difference between Bianconi and ToE is subtle but decisive:
- Bianconi uses entropy to compare metrics. Gravity emerges from mismatch.

- ToE uses entropy to generate metrics, motion, and observation. Reality emerges from entropy itself.

In Bianconi’s world, entropy is a tool. In ToE’s world, entropy is the field.

Why ToE Is Original and Useful

ToE’s originality lies in its ontological inversion. It dethrones the observer, making relativity emergent from entropy rather than fundamental. It reframes spacetime, motion, and causality as consequences of entropy’s finite-rate dynamics.

Its usefulness lies in its unification power:

- A field-theoretic origin of relativity, quantum coherence, and spacetime geometry

- A natural explanation for dark matter and dark energy via entropic vacuum pressure

- A new lens on time’s arrow, causality, and the emergence of physical law
Where Bianconi reformulates gravity, ToE reconstructs physics itself.

Conclusion:

Entropy as the Fabric of Reality

Both Bianconi and Obidi are pioneers in the entropic turn of physics. Bianconi shows that gravity can be understood through entropy. Obidi shows that reality itself can be understood as entropy.

The difference is not just technical—it is philosophical. In ToE, entropy is not a measure of reality. It is the fabric of reality.

If ToE succeeds, it will mark a turning point: relativity, quantum mechanics, and spacetime itself will be seen not as fundamental, but as emergent from the entropic field.
And that is why ToE is more than a comparison. It is a reconstruction.

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