Progress of the Theory of Entropicity (ToE): Literature on Novel Derivations of Einstein's Relativistic Kinematics and General Relativity in Modern Theoretical Physics 

The Theory of Entropicity (ToE) emerges within a growing but still fragmented body of work exploring thermodynamic, informational, and entropic origins of relativistic physics. While several authors have proposed partial connections between entropy, spacetime geometry, and relativistic kinematics, none provide a unified, first‑principles derivation that treats entropy density, entropy conservation, and the entropic field as the fundamental substrate from which relativistic effects and spacetime structure emerge.

The ToE positions itself as the first framework to derive:

- relativistic kinematics  

- gravitational curvature  

- time dilation  

- length contraction  

- mass variation  

- and deviations when the speed of light \(c\) is not constant  

directly from entropic field dynamics rather than from postulated invariances or geometric axioms.

This places the ToE in dialogue with — but distinct from — several modern research threads.

Methodology of the Theory of Entropicity (ToE)

The ToE is built on three methodological pillars:

1. The Entropy Field

A continuous field \(S(x)\) defined over an underlying information‑geometric manifold.  

This field encodes:

- local entropy density  

- entropic gradients  

- entropic curvature  

- the directionality of time  

2. The Conservation Principle

A fundamental conservation law:

\[

\nabla\mu J^\muS = 0

\]

where \(J^\mu_S\) is the entropy current.  

This replaces the postulate of invariant light speed with a deeper invariant: entropy flow cannot be destroyed, only redistributed.

3. Entropy Density and Relativistic Effects

Relativistic kinematics arise as emergent constraints on how entropy can redistribute under motion.  

From this, the ToE derives:

- time dilation as reduced entropy‑update rate  

- length contraction as compression of entropic degrees of freedom  

- mass increase as entropic curvature density  

- relativistic momentum as resistance to entropy reconfiguration  

A key prediction of the ToE is that if the speed of light \(c\) varies, the relativistic transformations deform in a precise, entropically determined way — connecting naturally to modified kinematics literature but grounded in a single entropic principle.

References and Historical Context

The ToE builds upon and extends several partial precedents:

Thermodynamic and Entropic Approaches

- Livadiotis & McComas (2025) — thermodynamic origins of relativity  

- Parker & Jeynes (2021) — entropic Hamiltonian dynamics  

- Chirco, Liberati & Relancio (2022) — spacetime thermodynamics  

- Bianconi (2025) — gravity from entropy  

These works hint at thermodynamic underlying relativity, but none derive the full relativistic framework from a single entropic field.

Information Geometry

- Amari (2016) — foundational information geometry  

The ToE uses information geometry not as a mathematical tool but as the substrate from which spacetime emerges.

Deformed and Modified Kinematics

- Carmona et al. (2019)  

- Pfeifer & Relancio (2022)  

- Russo & Townsend (2009)  

- Sahoo (2016)  

These works explore modified Lorentz transformations and deformed relativistic kinematics, but they lack a unifying physical principle.  

The ToE provides that principle: entropic curvature.

Arrow of Time

- Carroll (2010) — thermodynamic arrow of time  

The ToE replaces the thermodynamic arrow with the entropic‑geometric arrow, derived from the monotonic increase of Fisher information.

The Obidi Contribution

- Obidi (2025–2026) — Theory of Entropicity  

Obidi’s work introduces:

- the Entropic Primacy Axiom  

- the Information‑Geometric Substrate Axiom  

- the Obidi Equivalence Principle (OEP):  

  spacetime is the macroscopic projection of the underlying information‑geometric manifold, with geometric curvature corresponding to entropic curvature.

This is the first framework to unify:

- entropy  

- information geometry  

- relativistic kinematics  

- gravitational curvature  

- and potential variations in \(c\)  

under a single, coherent principle.

 📚 Context from Literature on the Novel Derivations of Einstein's Relativistic Kinematics and General Relativity: Progress of the Theory of Entropicity (ToE)

Methodology of the Theory of Entropicity (ToE)

1. Entropy field + conservation principle + density
2. Derivation of relativistic effects (time dilation, length contraction, mass increase)
3. A deviation when the speed of light c changes

References and Historical Context 

Some partial parallels exist, but none match ToE's full claim:

1. Libations, G. (2025). Thermodynamic origins of relativity. Scientific Reports.
2. Parker & Jeynes (2021). Entropic relativistic dynamics. Universe.
3. Chirco et al. (2022). Spacetime thermodynamics. arXiv.
4. Bianconi (2025). Gravity from entropy. Phys. Rev. D.
5. Amari (2016). Information Geometry.
6. Carmona et al. (2019). Deformed relativistic kinematics.
7. Pfeifer & Relancio (2022). Modified kinematics.
8. Russo & Townsend (2009). Relativistic motion.
9. Carroll (2010). Arrow of time.
10. Obidi (2025–2026). Theory of Entropicity (ToE).

📚 Key References

1. Livadiotis, G., & McComas, D. (2025). Thermodynamic and kinematic origins of relativity. Scientific Reports.
2. Parker, M. C., & Jeynes, C. (2021). Relativistic entropic Hamiltonian. Universe.
3. Chirco, G., Liberati, S., & Relancio, J. (2022). Spacetime thermodynamics. arXiv.
4. Pfeifer, C., & Relancio, J. (2022). Deformed relativistic kinematics. EPJC.
5. Russo, J. G., & Townsend, P. K. (2009). Relativistic kinematics. J. Phys. A.
6. Sahoo, R. (2016). Relativistic kinematics. arXiv.
7. Carmona, J. M. et al. (2019). Deformations of relativistic kinematics. Symmetry.
8. Carrera, M. (2010). Geometrical methods in relativity.
9. Bianconi, G. (2025). Gravity from entropy.
10. Obidi, J. O. (2025–2026). Theory of Entropicity.

The Iteration Revolution: Why Modern Theoretical Physics Must Adopt the Software Model — A Publication Manifesto for the Theory of Entropicity (ToE)

---

For more than a century, theoretical physics has operated inside a publication architecture inherited from the age of printing presses, academic gatekeeping, and slow‑moving institutions. Papers take months — sometimes years — to pass through anonymous reviewers, editorial committees, and prestige‑driven filters before they are allowed to “exist” in the scientific record.

This model once made sense.
Today, it is an anachronism.

In an era where software engineers deploy updates to millions of users in minutes, where open‑source communities iterate faster than corporations, and where knowledge moves at the speed of networks, physics remains trapped in a workflow designed for the 19th century.

The result is predictable:

• paradigm shifts are delayed
• bold ideas are discouraged
• innovation is throttled
• young thinkers are filtered out
• consensus ossifies faster than it evolves

The Theory of Entropicity (ToE) — a framework built on emergence, information geometry, and entropic primacy — cannot be born inside such a system.
It requires a different publication model entirely.

It requires the software iteration model.

---

1. The Old Model: Slow, Gatekept, and Prestige‑Driven

Traditional academic publishing is built on a cathedral‑style architecture:

• centralized authority
• slow review cycles
• anonymous gatekeepers
• prestige hierarchies
• rigid formatting
• limited distribution
• paywalls

This model assumes:

• knowledge must be filtered before it is shared
• authority must precede visibility
• consensus must precede innovation

But physics has reached a point where the bottleneck is not knowledge — it is the system that distributes it.

Theories do not fail because they are wrong.
They fail because they cannot survive the publication pipeline.

---

2. The Software Model: Fast, Open, Iterative, Evolutionary

Software engineering solved this problem decades ago.

Instead of cathedral‑style development, it embraced the bazaar model:

• rapid iteration
• version control
• open collaboration
• continuous deployment
• public feedback
• transparent improvement
• decentralized contribution

Progress accelerated not because developers became smarter, but because iteration cycles shrank.

Physics has never adopted this mindset — but it must.

---

3. Why Theoretical Physics Needs Iteration, Not Permission

Theories are not sacred texts.
They are living systems.

They evolve through:

• refinement
• correction
• contradiction
• extension
• falsification
• reinterpretation

But the current publication model treats theories as static artifacts that must be “perfect” before release.

This is the opposite of how discovery works.

The Theory of Entropicity (ToE) — with its emphasis on emergence, information geometry, and entropic curvature — is not a single paper.
It is a versioned system.

It must evolve like software:

• ToE v0.1
• ToE v0.2
• ToE v1.0
• ToE v2.0
• ToE v3.4.1 (patch for the Obidi Equivalence Principle)

This is how ideas grow.

This is how paradigms shift.

This is how physics moves forward.

---

4. The Obidi Principle of Scientific Iteration

If the Obidi Equivalence Principle states that:

Spacetime emerges from information geometry,

then the Obidi Principle of Scientific Iteration states:

Scientific progress emerges from rapid, open, iterative refinement — not from slow, closed, prestige‑driven approval.

The two principles mirror each other:

• emergence over authority
• iteration over perfection
• openness over gatekeeping
• evolution over stagnation

The ToE is not just a theory of physics.
It is a theory of how physics should be done.

---

5. The New Publication Model for the Theory of Entropicity

A modern scientific workflow should look like this:

1. Publish early

Release the idea before it is “perfect.”

2. Iterate publicly

Every refinement is a version update.

3. Accept open critique

Not anonymous gatekeeping — transparent feedback.

4. Use version control

The theory evolves like a codebase.

5. Maintain a changelog

Every correction is documented.

6. Encourage forks

Alternative formulations are not threats — they are contributions.

7. Let experiments, not reviewers, be the judge

Reality is the only peer reviewer that matters.

This is not chaos.
This is scientific evolution at the speed of networks.

---

6. Why the Theory of Entropicity Demands This Model

The ToE is not incremental.
It is not a small correction to existing frameworks.
It is a structural re‑architecture of physics:

• entropy as the fundamental invariant
• information geometry as the substrate
• spacetime as an emergent projection
• gravity as entropic curvature
• time as information ordering

Such a theory cannot be birthed inside a system designed to protect the status quo.

It must be developed in the open, iteratively, collaboratively — like software.

The ToE is not just a theory of the universe.
It is a theory of how to build theories.

---

7. The Future of Physics Belongs to the Iterators

The next Einstein will not wait 18 months for peer review.
The next Dirac will not ask permission to publish.
The next Feynman will not submit to anonymous gatekeepers.

The next revolution in physics will come from thinkers who:

• publish early
• iterate fast
• collaborate openly
• refine continuously
• treat theories as evolving systems

The Theory of Entropicity  (ToE) is one such revolution.

And it requires a publication model worthy of its ambition.

---

The New Physics in the Theory of Entropicity (ToE)

The Theory of Entropicity (ToE) is a radical and emerging framework in theoretical physics, originated by John Onimisi Obidi in 2025. Its central, revolutionary claim is that **entropy is not merely a measure of disorder—it is the fundamental field of reality itself**, the dynamic substrate from which space, time, gravity, quantum mechanics, and all physical phenomena emerge [[1]].

"Entropy is not a measure of disorder. It is the heartbeat of existence itself." — John Onimisi Obidi

🔑 Core Principles

1. Entropy as an Ontological Field

Unlike conventional physics where entropy is a secondary statistical concept, ToE elevates entropy to an ontological scalar field denoted *S(x,t)* that:

- Permeates all of existence at every point in space and time

- Drives all physical interactions through its gradients and curvature

- Replaces spacetime geometry as the fundamental substrate of reality [[1]]

2. The Speed of Light as an Entropic Rate

The universal constant *c* is reinterpreted not as a postulate about photons, but as **the maximum rate at which the entropic field can reorganize energy and information**. Light is simply the visible manifestation of this maximum entropic reconfiguration speed [[2]].

3. The "No-Rush Theorem" (G/NCBR)

All physical interactions require a finite, non-zero time for the entropic field to redistribute and synchronize states. This provides a physical grounding for causality and the universal speed limit—nothing can outpace the field's own rearrangement rate [[1]].

4. Emergent Gravity

Gravity is not a fundamental force but **emerges from the entropic field's statistical tendency to maximize entropy**. Matter is conceptualized as "frozen entropy" or stable entropic excitations—localized regions of entropic condensation [[4]].

5. Emergent Spacetime

Space and time are not fundamental containers:

- Time emerges from the directional flow of entropy

- Space is a map of entropic gradients

- Motion happens when the entropic field reconfigures gradients toward equilibrium [[1]]

🧮 Mathematical Framework

ToE introduces the **Entropic Metric Equation**, extending information geometry:

> *gᵢⱼ^(α) = ∂²ψ(θ)/∂θᵢ∂θⱼ + α Tᵢⱼₖ(θ)*

In this formulation:

- The potential *ψ(θ)* becomes the **entropy potential field** that drives time and structure

- The tensor *Tᵢⱼₖ(θ)* becomes the **irreversibility tensor**, encoding the arrow of time

- The constant *α* becomes a **physical curvature constant of entropy** [[5]]

The theory also introduces:

- **The Obidi Action**: A variational principle governing entropy dynamics

- **Master Entropic Equation (MEE)**: Governing field equations

- **Entropic Geodesics**: Paths of maximum entropy flow

- **Entropic Lorentz Factor (γₑ)**: Derived from entropic invariants rather than postulated [[3]]

🔬 Deriving Relativistic Effects

One of ToE's major claims is that it **derives Einstein's relativistic phenomena from entropic principles** rather than geometric postulates:

| Effect | ToE Explanation |

|--------|----------------|

| Mass Increase | Entropy density increases with velocity; since mass ∝ entropy density, *m(v) = γₑm₀* |

| Time Dilation | A clock's tick requires fixed entropic budget; higher entropy density stretches the period: *τ(v) = γₑτ₀* |

| Length Contraction | Total entropy of a rod is conserved; increased entropy density requires shorter length: *L(v) = L₀/γₑ* |

The Entropic Resistance Principle (ERP) explains why additional entropy must be expended to increase velocity, leading directly to observed relativistic effects [[3]].

🌐 Unification Attempt 

ToE aims to unify:

- Thermodynamics (entropy as fundamental)

- Relativity (deriving Lorentz transformations from entropic conservation)

- Quantum Mechanics (via the Vuli–Ndlela Integral, an entropy-weighted path integral)

- Information Theory (through Amari–Čencov α-connection formalism) [[5]]

The theory proposes that Tsallis' and Rényi's entropy formulations emerge as natural consequences of the same underlying α-curvature in the entropic field.

⚠️ Current Status & Considerations

- ToE is a **very recent framework** (originated 2025) and remains **emerging and yet to be widely accepted** in mainstream physics

- Most publications appear on preprint servers (Cambridge Open Engage, ResearchGate, Medium) and yet to be fully peer-reviewed

- The theory makes testable predictions: if the entropic propagation speed *cₑ* differs from *c*, measurable deviations from standard relativity would appear [[3]]

- The Theory of Entropicity (ToE) builds upon but significantly extends earlier ideas like entropic gravity (Verlinde) and entropic dynamics (Caticha), claiming to go beyond them by treating entropy as ontological rather than epistemic [[1]]

📚 Key Resources

- Original papers by John Onimisi Obidi on Cambridge Open Engage [[2]][[3]]

- Conceptual introductions on Medium [[1]][[4]]

- Encyclopedia entries summarizing the framework [[5]]

*Note: As an emerging theoretical framework, ToE is being approached with scientific scrutiny. Its claims call for rigorous peer review and experimental validation prior to acceptance as established physics.*

References 

1)

https://medium.com/@jonimisiobidi/the-new-physics-in-the-theory-of-entropicity-toe-f0c4aa4d60bc

2)

https://theoryofentropicity.blogspot.com/2026/04/the-new-physics-in-theory-of.html

3)

http://youtube.com/post/Ugkx6Hb-AzbRoh6_ENjz1CcXDv7VqpDiZ1rS?si=4E63qyPA5QqipnZJ

On the Mathematical Foundation of the Theory of Entropicity (ToE): The Historical Reflection, Logical Motivation, and Conceptual Leap in Relation to Contemporary Researchers and Investigators 

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🧠 Collective Insight Summary

The researchers mentioned below:

• Amari (2016)
• Anza & Crutchfield (2022)
• Franzosi et al. (2016)

all establish an important fact:

Entropy and information naturally generate geometric structures.

But they stop at geometry as a mathematical or descriptive tool.

---

👉 What  ToE (Obidi)  has done is fundamentally different:

Obidi is not using information geometry to describe systems —
Obidi is asserting that information geometry is physical reality itself.

That is the key distinction.

---

🔍 What Existing Researchers Have Actually Done 

1. Amari (2016) — Information Geometry

• Shows:
  • Fisher information defines a Riemannian metric
  • Probability distributions form statistical manifolds

👉 But:

• This geometry lives in parameter space, not spacetime
• It is a tool for inference and statistics

📌 It does NOT claim:

spacetime = Fisher geometry

---

2. Anza & Crutchfield (2022) — Entropy & Geometry

• Connect:
  • entropy
  • information dimension
  • geometric structure

👉 But:

• Focus is on quantum systems and complexity
• Geometry is derived from informational properties

📌 Again:

geometry is descriptive, not ontological

---

3. Franzosi et al. (2016) — Geometric Entropy

• Define:
  • entropy measures based on curvature of manifolds

👉 But:

• Applied to:
  • networks
  • complex systems

📌 Geometry is:

a way to measure complexity, not the fabric of spacetime

---

🔥 What Obidi Has Done That Is Different

---

⭐ 1. Obidi Made an Ontological Leap

Others:

Information geometry describes systems

Obidi:

Information geometry is the substrate of reality

That is a category shift, not just an extension.

---

⭐ 2. Obidi Imposed a Full Equivalence [the Obidi Equivalence Principle (OEP)]

Others:

• Explore relationships:
  • entropy ↔ geometry
  • information ↔ structure

Obidi:

Demands a one-to-one correspondence (isomorphism):

(\mathcal{M}_{info}, g_F) \leftrightarrow (\mathcal{M}_{spacetime}, g_{\mu\nu})

👉 No one in mainstream literature enforces this as a strict principle.

---

⭐ 3. Obidi Promotes Geometry → Physics

Others:

• Geometry = mathematical structure

Obidi:

• Geometry = physical dynamics

Specifically:

• geodesics → physical motion
• curvature → gravity
• entropy flow → time evolution

---

⭐ 4. Obidi Closes the Loop with an Action Principle

Others:

• Do not generally provide:
  • a full field theory based on entropy geometry

Obidi:

• Introduce:
  • entropic action
  • field equations (MEE)

👉 This attempts to turn:

information geometry → dynamical physics

---

⭐ 5. Obidi Eliminates Dualism

Most research still has:

Layer	Role
Physical spacetime	real
Information geometry	descriptive

---

Obidi replaces this with:

Single Layer
Information geometry = spacetime

👉 That’s a monistic framework, not dual.

---

⚖️ Statement of the Difference

Here, we state the essential difference between what Obidi has done and what other researchers and investigators have done:

Existing research shows that entropy and information can be represented geometrically. 

The Theory of Entropicity (ToE) goes further by asserting that this information geometry is not merely representational but is physically real, and that spacetime itself is an emergent, isomorphic projection of this underlying entropic manifold governed by its own action and field equations.

---

Obidi's Challenge and Responsibility 

This distinction made by Obidi is indeed real—but it comes with audacious responsibility and ontological courage.

---

1. Obidi Made a Stronger Claim Than Others

They say:

• “geometry models information”

Obidi says:

• “geometry is reality”

👉 That requires:

• stricter proof
• stronger constraints

---

2. Obidi Introduced Isomorphism (Very Strong)

Most researchers avoid claiming:

• invertible mapping
• full preservation of structure

👉 Because this is extremely hard to justify mathematically.

---

3. Obidi Enters the “Theory of Everything” Zone

By unifying:

• spacetime
• entropy
• information

👉 Obidi's ToE is competing with:

• GR
• QFT
• quantum gravity programs

Principles of Physics as Re‑conceptualized from the Foundations of the Theory of Entropicity (ToE)

Preamble 

The Theory of Entropicity (ToE), developed by John Onimisi Obidi, proposes a fundamental re‑conceptualization of physical ontology by elevating entropy from a statistical descriptor to the primary dynamical field of the universe. This paper reconstructs the principles of physics from the ground up using the entropic field as the foundational substrate. Classical notions of spacetime, matter, force, causality, and measurement are reinterpreted as emergent consequences of entropic curvature and finite‑rate entropic propagation. The resulting framework unifies metaphysics, epistemology, and physics into a single entropic ontology, offering a coherent alternative to the geometric foundations of general relativity and the probabilistic foundations of quantum mechanics.

1. Introduction: The Need for a New Foundation

Modern physics rests on three monumental pillars: quantum mechanics, general relativity, and thermodynamics. Each is internally consistent, yet their conceptual foundations remain mutually incompatible. Quantum mechanics describes microscopic behavior through probabilistic amplitudes; general relativity describes macroscopic structure through geometric curvature; thermodynamics describes macroscopic irreversibility through entropy. The absence of a unified ontological basis has led to decades of attempts at reconciliation, from quantum gravity to emergent spacetime models.

The Theory of Entropicity (ToE) proposes that the incompatibility arises because physics has been built on the wrong primitives. Instead of geometry, particles, or fields, the ToE asserts that entropy is the fundamental ontological entity. All other structures—spacetime, matter, classicality, and even time itself—emerge from the evolution of the entropic field.

This paper articulates the principles of physics as reconstructed from this entropic foundation.

2. The Entropic Field as the Fundamental Ontological Substrate

2.1 From Statistical Quantity to Physical Field

In classical thermodynamics, entropy measures disorder; in statistical mechanics, it quantifies microstate multiplicity; in information theory, it measures uncertainty. None of these interpretations treat entropy as a physical field with causal power. The ToE departs from this tradition by asserting that entropy is not a descriptor but a primitive dynamical field, denoted \( F_E \).

The entropic field possesses curvature, gradients, and propagation rules. It is continuous, universal, and irreducible. All physical phenomena arise from its structure and evolution.

2.2 Entropic Curvature and the Structure of Reality

Curvature in the entropic field determines the distinguishability of physical configurations. Regions of high entropic curvature give rise to stable classical structures; regions of low curvature correspond to quantum indeterminacy. The universe is thus a tapestry woven from entropic gradients, not geometric manifolds.

3. Reconstruction of Spacetime from Entropic Dynamics

3.1 Spacetime as an Emergent Construct

In general relativity, spacetime is a geometric manifold whose curvature determines gravitational behavior. In the ToE, spacetime is not fundamental. It emerges from the organization of entropic gradients. The metric structure of spacetime is a secondary effect of the entropic field’s internal dynamics.

3.2 Finite‑Rate Entropic Propagation and the Arrow of Time

The entropic field evolves at a finite rate, establishing a universal temporal ordering. Time is not a dimension but a measure of entropic redistribution. The arrow of time arises naturally from the irreversibility of entropic evolution, eliminating the need for external temporal assumptions.

4. Matter, Forces, and Classicality as Entropic Phenomena

4.1 Matter as Stabilized Entropic Configurations

Particles are not fundamental entities but stable entropic knots—localized regions where entropic gradients maintain persistent identity. Their properties (mass, charge, spin) correspond to invariants of entropic curvature.

4.2 Forces as Entropic Interactions

Interactions between particles arise from the tendency of the entropic field to redistribute curvature. What we call “forces” are manifestations of entropic equilibration. Gravity, in particular, is the macroscopic expression of entropic curvature, not a geometric deformation of spacetime.

4.3 Classicality as Entropic Stabilization

Classical behavior emerges when entropic gradients reach thresholds that allow distinguishability. Measurement is the entropic stabilization of a system’s configuration, not an act of observation.

5. The Obidi Action: Governing the Dynamics of the Entropic Field

5.1 Variational Foundations

The Obidi Action is the variational principle that governs the evolution of the entropic field. It plays a role analogous to the Einstein–Hilbert action in general relativity but operates on entropic curvature rather than geometric curvature.

5.2 Universality Across Physical Regimes

The Obidi Action applies uniformly across all scales—quantum, classical, and cosmological. This universality eliminates the need for separate frameworks for different physical domains.

6. The No‑Go Theorem (NGT): Entropy as the Arbiter of Physical Law

The No‑Go Theorem states that any proposed physical law \( L \) that contradicts the entropic field collapses into inconsistency:

\[

L \land F_E = \bot

\]

This principle establishes the entropic field as the ultimate filter of physical admissibility. Laws that violate entropic constraints cannot exist in any coherent universe.

7. Epistemology Reconstructed: Entropology and the Physics of Knowing

7.1 Knowledge as Entropic Structure

In the ToE, knowing is not a mental abstraction but a physical process. Information is entropic structure; cognition is entropic negotiation between subsystems.

7.2 The Observer as a Local Entropic Subsystem

The observer is not metaphysically privileged. Observation does not create reality; it registers entropic stabilization. This resolves long‑standing paradoxes in quantum mechanics by removing the observer from the center of physical ontology.

8. The Universe as a Self‑Adjusting Entropic Continuum

The ToE portrays the universe as a dynamic, self‑organizing continuum. It evolves by redistributing entropy, increasing distinguishability, and stabilizing structure. The cosmos “learns” through entropic evolution, continually refining its internal organization.

This perspective unifies cosmology, quantum theory, and thermodynamics under a single entropic principle.

9. Implications for the Future of Physics

Reconstructing physics from the entropic field has profound implications:

- It offers a unified foundation for all physical laws.  

- It resolves the conceptual tension between quantum mechanics and general relativity.  

- It reframes time, gravity, and measurement as emergent phenomena.  

- It provides a new ontology for scientific inquiry.  

The ToE thus represents not merely a new theory but a new worldview—one in which entropy is the engine of existence.

10. Conclusion

The Theory of Entropicity redefines the principles of physics by grounding them in the dynamics of the entropic field. Spacetime, matter, forces, classicality, and knowledge emerge from entropic curvature and finite‑rate entropic propagation. This reconstruction unifies the conceptual foundations of physics and offers a coherent alternative to geometry‑based and probability‑based ontologies.

The entropic field becomes the fundamental reality; everything else is its unfolding.

⭐ The Obidi Equivalence Principle (OEP) of the Theory of Entropicity (ToE)

Spacetime is the macroscopic projection of an underlying information‑geometric manifold, and every geometric property of physical spacetime corresponds to an entropic property of that information manifold.

More formally:

> The curvature, geodesics, and metric structure of physical spacetime arise from, and are isomorphic to, the curvature, geodesics, and Fisher‑information metric of the underlying information‑geometric manifold after coarse‑graining.

The Obidi Equivalence Principle proposes a global isomorphism between an underlying information-geometric manifold endowed with a Fisher metric and emergent physical spacetime, asserting that all geometric and dynamical properties of spacetime correspond to entropic and informational structures under a coarse-graining map.

🧠 Collective Historical Insight Summary

What ToE has formulated as the Obidi Equivalence Principle (OEP) is essentially an attempt to do for entropy/information what Einstein did for gravity:

Establish a strict equivalence (isomorphism) between two domains:

1) information geometry

2) physical spacetime geometry

This idea does have precedents in fragments across physics:

holography (geometry ↔ entanglement)

AdS/CFT (bulk ↔ boundary)

information geometry (Fisher metric ↔ statistical structure)

But:

👉 No mainstream framework currently enforces a full, global, invertible isomorphism of the kind which Obidi's Theory of Entropicity (ToE) has demanded.

So ToE's OEP is:

not baseless

but much stronger than anything currently accepted in traditional physics.

✅ Legitimacy of the Use of the Fisher Information Metric in the Theory of Entropicity (ToE)

From established literature:

Amari (2016) shows Fisher information defines a Riemannian metric

Anza & Crutchfield (2022) connect entropy and geometric structure

Franzosi et al. (2016) define geometric entropy via curvature

👉 So ToE's starting point:

“information → geometry”

is fully grounded in existing research

✅ ToE is Attempting a True Equivalence Principle

This is both important and audacious at once.

Compare:

Einstein EP

ToE's OEP

gravity ≡ geometry (Einstein)

spacetime ≡ information geometry (Obidi)

inertial = gravitational mass  (Einstein)

physical = entropic geometry (Obidi)

local equivalence  (Einstein)

global mapping (Obidi)

👉 Structurally, this is the right kind of move for a foundational theory.

This is the core demand of the Theory of Entropicity (ToE):

\[

(\mathcal{M}{info}, g{F}) \;\xrightarrow{\text{emergence}}\; (\mathcal{M}{spacetime}, g{\mu\nu})

\]

with the requirement that:

\[

\Phi: \mathcal{M}{info} \to \mathcal{M}{spacetime}

\]

is a smooth, invertible mapping preserving curvature, geodesics, and entropy production.

That is:

Emergence relation:

(𝓜₍ᵢₙfₒ₎, gF) ⟶₍ₑₘₑᵣgₑₙcₑ₎ (𝓜₍ₛₚₐcₑₜᵢₘₑ₎, gμν)

Correspondence map:

Φ : 𝓜₍ᵢₙfₒ₎ → 𝓜₍ₛₚₐcₑₜᵢₘₑ₎

⭐ What the principle asserts (in plain language)

1. Information geometry is the substrate.  

   It exists before spacetime.

2. Spacetime emerges from information geometry.  

   Not as a metaphor — as a coarse‑grained projection.

3. Every physical geometric quantity has an entropic counterpart.  

   - Spacetime curvature ↔ Entropic curvature  

   - Geodesics ↔ Paths of extremal entropy flow  

   - Mass ↔ Information‑curvature density  

   - Energy ↔ Rate of information change  

4. Gravity is not a force but an entropic gradient.  

   This is the entropic analogue of Einstein’s “gravity = geometry.”

5. The arrow of time is the monotonic increase of Fisher information.

⭐ Why this principle is necessary for the Theory of Entropicity (ToE)

Without the OEP:

- spacetime and information geometry become dualistic  

- entropy cannot be the fundamental invariant  

- gravity cannot be entropic  

- quantum mechanics cannot be geometric  

- the ToE collapses into two incompatible layers  

With the Obidi Equivalence Principle (OEP):

- quantum → statistical geometry  

- gravity → entropic curvature  

- time → information ordering  

- energy → information flow  

- spacetime → emergent macro‑geometry  

Everything becomes one coherent structure.

⭐ The 3 Axioms of the Theory of Entropicity (ToE):

- Axiom 1: Entropic Primacy  

- Axiom 2: Information‑Geometric Substrate  

- Axiom 3: Obidi Equivalence Principle (OEP)  

References 

1)

https://theoryofentropicity.blogspot.com/2026/04/obidi-equivalence-principle-oep.html

2)

http://youtube.com/post/UgkxMndtJGNXut5AISg1-2nRtwCBDUmhkxYM?si=xnYZNWea-SgUSb9M

3)

https://medium.com/@jonimisiobidi/the-obidi-equivalence-principle-oep-of-the-theory-of-entropicity-toe-8ff4c199a3d7