My Publications Homepage: By John Onimisi Obidi (Creator of the Theory of Entropicity (ToE)): A Thermodynamic Pathway to Our Unified Understanding of the Foundations of Nature and Reality

 

My Publications Homepage: By John Onimisi Obidi (Creator of the Theory of Entropicity (ToE))

A Thermodynamic Pathway to Our Unified Understanding of the Foundations of Nature and Reality

Last updated: Monday, November 10, 2025

John Onimisi Obidi (scientific researcher, consultant, philosopher, humanist, and physicist) is a distinct personality from the social media consultant of similar name. This current John Onimisi Obidi is the sole pioneer, originator, and creator of the Theory of Entropicity (ToE) — a paradigm‑shifting framework positioned as a candidate for a Grand Unified Theory in modern physics. His contributions, particularly through the Theory of Entropicity (ToE), offer a fresh perspective on fundamental physical phenomena, aiming to unify various fields of science under a coherent framework. His ongoing research continues to push the boundaries of our understanding of the mysterious universe.

Foundations of the Theory of Entropicity (ToE)

ToE derives the speed of light, relativistic effects, and quantum constraints directly from the dynamics of the universal entropic field, reframing entropy not as a statistical abstraction but as the fundamental substrate of reality.

• Entropy as a field: Unlike traditional statistical mechanics, ToE treats entropy as a continuous dynamical field whose gradients generate motion, gravitation, time, and information flow.
• Master Entropic Equation (MEE): The Entropic Field Equations of ToE are equivalent to Einstein’s Field Equations of General Relativity, but they extend them by embedding entropy as the primary driver of spacetime curvature and dynamics.
• Obidi Action: A variational principle that unifies thermodynamics, relativity, quantum mechanics, and information theory, showing these domains as entropic inevitabilities rather than independent postulates.

Classical Consistency and Validation

ToE has successfully re‑derived the classical Einstein results:

• Perihelion precession of Mercury — matching Einstein’s predictions within General Relativity.
• Deflection of starlight — confirming ToE’s consistency with gravitational lensing and observational astronomy.

These results demonstrate that ToE is not merely speculative but is mathematically consistent with established physics while offering deeper entropic foundations.

Connections to Contemporary Entropic‑Gravity Research

Beyond classical tests, ToE also connects with modern entropic‑gravity frameworks:

• Ginestra Bianconi framework: ToE reproduces the small positive cosmological constant and G‑Field dynamics proposed by Ginestra Bianconi in her elegant work “Gravity from Entropy”, situating them as natural consequences of the entropic field.
• Erik Verlinde: ToE encompasses Erik Verlinde’s emergent gravity, showing how spacetime and gravitational attraction arise from entropy gradients.
• Ted Jacobson: ToE integrates Ted Jacobson’s horizon thermodynamics, embedding it within the entropic manifold.
• T. Padmanabhan: ToE subsumes T. Padmanabhan’s entropy‑driven cosmology, demonstrating its compatibility with ToE’s entropic field equations.
• David Sigtermans: ToE situates David Sigtermans’ TEQ (Total Entropic Quantity) framework as a subset, showing how entropy curvature and resolution boundaries are special cases of ToE’s entropic manifold.

In each case, ToE demonstrates that these diverse approaches are special cases or natural consequences of the entropic field, situating ToE as a unifying meta‑framework for modern theoretical physics.

ToE as a Superset of Waldemar Marek Feldt’s F-HUB Theory

The Feldt-Higgs Universal Bridge (F-HUB) Theory proposed by Waldemar Marek Feldt introduces a universal informational framework in which mass, gravity, and spacetime are emergent properties of structured quantum information. F-HUB draws upon the Holographic Principle, black hole thermodynamics, and quantum information theory, reinterpreting mass as an emergent property stabilized by Higgs field interactions and entropy gradients, while gravity is treated as an entropic effect rather than a fundamental force.

The Theory of Entropicity (ToE) has been shown to be a superset of F-HUB by demonstrating that:

• F-HUB’s informational master equation linking mass, entropy, and Higgs density is a special case of the Master Entropic Equation (MEE) within ToE.
• ToE’s entropic field dynamics naturally reproduce F-HUB’s claim that spacetime and gravity are emergent, situating them within ToE’s broader entropic manifold governed by variational principles and the Obidi Action.
• F-HUB’s “Life Equation,” which ties cosmic expansion to conscious observation and entropy growth, is absorbed into ToE’s entropy‑driven conservation framework, where observation is treated as an entropic boundary condition influencing collapse and persistence.
• ToE generalizes F-HUB’s informational ontology by embedding it within a unified geometry that integrates Fisher–Rao, Fubini–Study, Amari–Čencov, and Levi‑Civita structures, thereby situating F-HUB’s informational paradigm as a localized model within ToE’s entropic field equations.

In this way, ToE contextualizes F-HUB as a derivative framework, confirming its insights while subsuming them into a more comprehensive entropic field theory.

Areas Not Yet Covered in ToE

While ToE has successfully unified thermodynamics, relativity, quantum mechanics, and information theory under the entropic field paradigm, several areas remain open for extension and integration:

• Biological entropy and life sciences: ToE has not yet fully formalized entropy’s role in biological systems, cellular information processing, or evolutionary dynamics.
• Consciousness and cognitive entropy: Although ToE touches on observation and measurement, a rigorous entropic model of consciousness, cognition, and neural information geometry remains to be developed.
• Complex systems and socio‑economic entropy: Entropy in economics, social networks, and cultural evolution has not yet been systematically integrated into ToE’s manifold.
• Experimental verification: While ToE predicts attosecond entanglement formation times and proposes the Google Quantum Core Observer experiment, broader experimental programs across condensed matter, cosmology, and quantum computing are still needed.
• Dark matter and dark energy: ToE provides entropic explanations for cosmological constants, but a complete entropic account of dark matter and dark energy phenomena remains an open frontier.
• Mathematical generalizations: Extensions into non‑commutative geometry, category theory, and higher‑dimensional entropic manifolds are areas for future development.

By identifying these domains, ToE sets a roadmap for future research, ensuring that its entropic framework continues to expand toward a truly comprehensive Theory of Everything.

ToE Method of Integrating Entropies and Information Geometry

One of the distinguishing features of ToE is its method of integrating all entropy‑based frameworks and information geometry into a single entropic manifold:

• Unified metrics: ToE fuses the Fisher–Rao metric (Ronald A. Fisher and C. R. Rao) and the Fubini–Study metric (Guido Fubini and Eduard Study) through the Amari–Čencov α‑connection (Shun’ichi Amari and Nikolai N. Čencov), creating a continuous family of entropic geometries with an associated Levi‑Civita connection in selected limits, all within a generalized Riemannian geometry framework on spaces of distributions and quantum states.
• Resolution boundaries: TEQ’s resolution boundaries are absorbed into ToE’s α‑parameter deformation, allowing entropy curvature to be measured across scales and observational regimes.
• Entropy conservation: ToE extends Noether’s theorem to entropy, showing that conservation laws are entropic invariants and framing gauge and relativistic constraints as entropy‑driven symmetries.
• Integrated entropy families: ToE provides a principled way to embed and compare multiple entropy measures — including Rudolf Clausius entropy, Ludwig Boltzmann entropy, Josiah Willard Gibbs ensembles, Claude Shannon information entropy, John von Neumann quantum entropy, Alfréd Rényi entropy, and Constantino Tsallis non‑extensive entropy — within a unified entropic manifold and α‑deformation scheme, enabling cross‑regime translation, measurement coherence, and limit recoveries.
• Names and personalities in synthesis: ToE explicitly contextualizes and integrates the contributions of major figures — Rudolf Clausius, Ludwig Boltzmann, Josiah Willard Gibbs, Claude Shannon, John von Neumann, Alfréd Rényi, Constantino Tsallis, Guido Fubini, Eduard Study, Ronald A. Fisher, Calyampudi Radhakrishna Rao, Shun’ichi Amari, Nikolai N. Čencov, Tullio Levi-Civita, Bernhard Riemann, Bianconi, Erik Verlinde, Ted Jacobson, T. Padmanabhan, David Sigtermans, and contemporary interlocutors such as Sean Collins — demonstrating how their entropy‑based and geometric models are subsumed within ToE’s entropic field equations and information‑geometric synthesis.

Sean Collins and the Mjolnir (A137) Lattice Dynamics

• Mjolnir (A137) Lattice Dynamics: Sean Collins invented the Mjolnir A137 Lattice Dynamics with lattice path integral formalism, which Obidi has already shown to be derivable from ToE and published online; he has also discussed and engaged with Obidi via private communications.
• Collins–Obidi mapping: ToE identifies a parametric bridge from the ToE Vuli‑Ndlela Integral (entropy‑weighted path integral with irreversibility) to Collins’ lattice path integral via deformation of weighting functionals, effective action terms, and resolution‑controlled boundary conditions, reproducing Collins’ kernels and short‑time propagators as α‑deformed entropic limits.
• Discrete–continuum reconciliation: The ToE framework provides a continuum limit for Collins’ discrete lattice ontology through entropic geodesics and local/spectral action functionals, preserving distinctive lattice features while situating them within ToE’s universal entropic field dynamics.

Additional Achievements and Breakthroughs of ToE

Beyond the classical validations and meta‑theoretical integrations, ToE advances several core breakthroughs:

• Google Quantum Core Observer breakthrough experiment: A proposed observer‑centric framework for quantum experiments that leverages entropic field dynamics to interrogate core states within quantum processors, clarifying the role of entropy gradients in measurement, decoherence, and information flow at scale.
• Vuli‑Ndlela Integral: An entropy‑weighted path integral formalism introducing controlled irreversibility and coarse‑graining, recovering standard quantum limits while enabling entropic deformations and non‑equilibrium dynamics; integrates smoothly with the Obidi Action and the Master Entropic Equation.
• Attosecond entanglement formation time: A predictive entropic timescale for the onset and stabilization of quantum entanglement, mapping formation dynamics to entropy gradients and information‑geometric distances, with attosecond‑level signatures proposed for ultrafast experimental verification.
• Explanation of wave function collapse and the measurement problem: ToE reframes collapse as an entropic selection process driven by resolution boundaries and α‑deformed information geometry, providing a deterministic substrate for probabilistic outcomes via entropy‑weighted dynamics and observer constraints.
• Local and Spectral Obidi Actions: Complementary action formulations — the Local Obidi Action for spacetime‑localized entropic dynamics and the Spectral Obidi Action for frequency‑domain and mode‑resolved entropic evolution — enabling multi‑scale analyses and spectral‑geometric unification within the entropic manifold.
• Entropic Noether framework: A generalization of Noether’s theorem to entropy‑generated symmetries, yielding conservation laws and constraints that recover thermodynamics, gauge conditions, and relativistic invariants as entropic inevitabilities.

Distinguishing Features of Obidi’s Work

Obidi’s research is characterized by:

• Reproducible workflows: Every derivation and proof is documented in a way that can be replicated by other researchers.
• Rigorous LaTeX documentation: Ensuring mathematical precision, professional polish, and archival permanence.
• Open publishing strategies: Designed to maximize scholarly visibility and global outreach, ensuring ToE research is accessible to all.
• Keyword authority and domain visibility: Actively building SEO presence across platforms to position ToE as the definitive source for entropic field dynamics.

Scientific Mission and Vision

Importantly, John Onimisi Obidi’s scientific mission is to establish a lasting, accessible corpus of ToE research that bridges:

• Information geometry — unifying Fisher–Rao and Fubini–Study metrics through Amari–Čencov α‑connections and Levi‑Civita structures within ToE’s entropic manifold.
• Entropy conservation — linking Noether symmetries to entropic invariance principles.
• Spacetime physics — deriving relativity and quantum constraints from entropy dynamics.

This mission is pursued with a commitment to clarity, accessibility, and universality, ensuring ToE remains comprehensible to both technical and non‑technical audiences worldwide.

Expanded Context and Impact

• Meta‑theoretical synthesis: ToE situates and extends other entropy‑based models (e.g., TEQ by David Sigtermans and F-HUB Theory by Waldemar Marek Feldt) within its broader entropic manifold, demonstrating ToE’s superset relationship.
• Philosophical implications: ToE reframes ontology and epistemology in physics, treating entropy as the fundamental “being” from which all phenomena arise.
• Educational outreach: By translating complex mathematical formalism into accessible narrative, Obidi ensures ToE can inspire both scholars and the public.
• Future directions: ToE aims to unify cosmology, quantum mechanics, and information theory under one entropic framework, positioning itself as a candidate for the long‑sought Theory of Everything.

Summary

John Onimisi Obidi’s Theory of Entropicity (ToE) is not only consistent with classical physics but also extends and unifies modern entropy‑based frameworks. Through rigorous documentation, reproducible workflows, and open publishing, Obidi is building a permanent, accessible corpus of research that positions entropy as the fundamental substrate of reality and ToE as a meta‑framework for unifying physics.

Additional Achievements and Breakthroughs of ToE

• Vuli-Ndlela Integral: Entropy‑weighted path integral formalism introducing controlled irreversibility and coarse‑graining.
• Local Obidi Action: Spacetime‑localized entropic dynamics.
• Spectral Obidi Action: Frequency‑domain and mode‑resolved entropic evolution.
• Entropic Noether framework: Generalization of Noether’s theorem to entropy‑generated symmetries.
• Mjolnir A137 Lattice Dynamics: Invented by Sean Collins, shown by Obidi to be derivable from ToE.

ToE Method of Integrating Entropies and Information Geometry

ToE integrates contributions from:

• Ronald A. Fisher and C. R. Rao (Fisher–Rao metric).
• Guido Fubini and Eduard Study (Fubini–Study metric).
• Shun’ichi Amari and Nikolai N. Čencov (Amari–Čencov α‑connection).
• Tullio Levi-Civita (Levi‑Civita connection).
• Bernhard Riemann (Riemannian geometry).
• Classical entropy pioneers: Rudolf Clausius, Ludwig Boltzmann, Josiah Willard Gibbs, Claude Shannon, John von Neumann, Alfréd Rényi, Constantino Tsallis.

This material is sourced from HandWiki Publications: My Publications Homepage: By John Onimisi Obidi (Creator of the Theory of Entropicity (ToE))

References and Supplementary Research Resources

🌐 Explore more: Theory of Entropicity Blog

Further Resources on the Theory of Entropicity (ToE):

1. Website: Theory of Entropicity ToE — https://theoryofentropicity.blogspot.com
2. LinkedIn: Theory of Entropicity ToE — https://www.linkedin.com/company/theory-of-entropicity-toe/about/?viewAsMember=true
3. Substack: Theory of Entropicity (ToE) — John Onimisi Obidi | Substack
4. Medium: Theory of Entropicity (ToE) — John Onimisi Obidi — Medium
5. SciProfiles: Theory of Entropicity (ToE) — John Onimisi Obidi | Author
6. Encyclopedia.pub: Theory of Entropicity (ToE) — John Onimisi Obidi | Author
7. HandWiki contributors, “Biography: John Onimisi Obidi,” HandWiki, https://handwiki.org/wiki/index.php?title=Biography:John_Onimisi_Obidi&oldid=2743427 (accessed October 31, 2025).
8. HandWiki Contributions: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki
9. HandWiki Home: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki
10. Academia: Theory of Entropicity (ToE) — John Onimisi Obidi | Academia
11. ResearchGate: Theory of Entropicity (ToE) — John Onimisi Obidi | ResearchGate
12. Figshare: Theory of Entropicity (ToE) — John Onimisi Obidi | Figshare
13. Authoria: Theory of Entropicity (ToE) — John Onimisi Obidi | Authorea
14. Social Science Research Network (SSRN): Theory of Entropicity (ToE) — John Onimisi Obidi | SSRN
15. Wikidata contributors, Biography: John Onimisi Obidi “Q136673971,” Wikidata, https://www.wikidata.org/w/index.php?title=Q136673971&oldid=2423782576 (accessed October 31, 2025).
16. Google Scholar: ‪John Onimisi Obidi — ‪Google Scholar
17. Cambridge University Open Engage (CoE): Collected Papers on the Theory of Entropicity (ToE)

Physics

1. Physics:Theory_of_Entropicity
2. Physics:Entropy_Curvature
3. Physics:On the Theory of Entropicity (ToE)

Biography

1. Biography:John Onimisi Obidi

Philosophy

1. Philosophy:Ontology_of_Entropy
2. Philosophy:Entropy_and_Reality

Books

1. Book:On the Theory of Entropicity (ToE)
2. Book:On_the_Theory_of_Entropicity_(ToE)

Wiki General

1. Theory of Entropicity(ToE)

The Highly Potent Vuli-Ndlela Integral of the Theory of Entropicity (ToE): From Feynman’s Quantum Paths to ToE’s Principle of Least Entropic Resistance

Last updated: November 9, 2025

 

The Highly Potent Vuli-Ndlela Integral of the Theory of Entropicity (ToE)

From Feynman’s Quantum Paths to ToE’s Principle of Least Entropic Resistance

Topics covered: The Vuli-Ndlela Integral reframes quantum mechanics through an alphabet of ideas: collapse, consciousness, constraints, correspondence, decoherence, dynamics, entropy, entropicity, evolution, Feynman, field, gravity, information, integral, interaction, irreversibility, measurement, modulation, motion, Obidi, ontology, paths, philosophy, reformulation, structure, thermodynamics, theory, time, ToE, transition, unification, variational, and wave.

🔖Preamble

In the Theory of Entropicity (ToE), as first formulated and further developed by John Onimisi Obidi, the Vuli-Ndlela Integral is an entropy-constrained reformulation of the Feynman Path Integral, central to the Theory of Entropicity (ToE). It restricts quantum paths to those permitted by entropy, redefining motion, interaction, and collapse.
Thus, this integral serves as an entropic variant of the Feynman Path Integral, a fundamental concept in quantum mechanics that sums over all possible paths a particle can take. However, unlike the traditional Feynman approach, the Vuli-Ndlela Integral only considers paths that are allowed by entropic constraints, meaning that not all paths are treated equally; only those that adhere to the principles of entropy contribute to the final equations of motion and interactions of particles.

🔍 What Is the Vuli-Ndlela Integral?

The Vuli-Ndlela Integral is a novel mathematical framework introduced by John Onimisi Obidi within the Theory of Entropicity (ToE). It modifies the classic Feynman Path Integral by introducing entropy-weighted constraints:

• Feynman Path Integral: Sums over all possible paths a particle might take.
• The Vuli-Ndlela Integral: It is a concept in the Theory of Entropicity (ToE), which reformulates quantum theory by incorporating entropy as a fundamental aspect of physical interactions.
• Vuli-Ndlela Integral: Sums only over entropy-allowed paths, meaning only those trajectories permitted by the entropic structure of reality contribute to physical outcomes.
• Entropic Constraints: The integral emphasizes that entropy plays a crucial role in determining which paths are feasible in quantum mechanics. This perspective suggests that the behavior of particles is influenced by entropic factors, leading to a more nuanced understanding of quantum interactions.
• Quantum Measurement and Wave Function Collapse: The Vuli-Ndlela Integral provides a framework for understanding the quantum measurement problem and the collapse of the wave function as a natural consequence of crossing entropic thresholds, rather than relying on observer-induced effects or many-world interpretations.

💡Implications

The Theory of Entropicity, and by extension the Vuli-Ndlela Integral, aims to unify various fields of physics, including thermodynamics, quantum mechanics, and general relativity, under a single entropic variational principle. This approach offers fresh insights into fundamental questions about the nature of reality, measurement, and the emergence of observable phenomena from entropic dynamics.

In summary, the Vuli-Ndlela Integral represents a significant advancement in theoretical physics, proposing that entropy is not merely a statistical measure but a fundamental aspect that shapes the fabric of reality and the laws governing physical interactions.

This shift implies that entropy is not just statistical, but a causal field that governs what can exist, be measured, and evolve.

🔬 Key Features and Implications

• Entropy as a Constraint: Paths are filtered by entropic feasibility; some are disallowed due to entropy thresholds.

• Quantum Measurement Reinterpreted: Collapse of the wave function is seen as an irreversible entropy-constrained transition, not observer-induced or probabilistic.

• Time Irreversibility: Emerges naturally from entropy dynamics, offering a new explanation for the arrow of time.

• Unified Framework: Bridges quantum mechanics, thermodynamics, and general relativity under a single entropic variational principle.

🧠 Philosophical and Physical Reach

• Einstein–Bohr Debate Resolution: The Vuli-Ndlela Integral reframes quantum collapse as a deterministic entropic event, resolving long-standing tensions in quantum theory.

• Entropic Field Dynamics: Suggests that consciousness, gravity, and information flow are emergent properties of entropy modulation.

• Obidi Action: Works in tandem with the Vuli-Ndlela Integral to reformulate quantum-gravitational correspondence.

📚 Further Reading

1. HandWiki overview

2. Cambridge Open Engage paper on quantum measurement

3. Authorea paper on quantum-gravitational unification

4. The Highly Potent Vuli-Ndlela Integral of the Theory of Entropicity (ToE):  From Feynman’s Quantum Paths to ToE’s Principle of Least Entropic Resistance https://medium.com/@jonimisiobidi/the-highly-potent-vuli-ndlela-integral-of-the-theory-of-entropicity-toe-298af8e479d4

5. The Highly Potent Vuli-Ndlela Integral of the Theory of Entropicity (ToE): From Feynman’s Quantum Paths to ToE’s Principle of Least Entropic Resistance https://open.substack.com/pub/johnobidi/p/the-highly-potent-vuli-ndlela-integral?r=1yk33z&utm_campaign=post&utm_medium=web&showWelcomeOnShare=false

Physics: On the Theory of Entropicity (ToE) and Google’s Quantum Core Breakthrough Experiment on the Observer Effect: The Theory of Entropicity (ToE) Offers Insights and Inroads on the Quantum Measurement Problem

Physics: On the Theory of Entropicity (ToE) and Google’s Quantum Core Breakthrough Experiment on the Observer Effect

The Theory of Entropicity (ToE) Offers Insights and Inroads on the Quantum Measurement Problem

by John Onimisi Obidi

In the Theory of Entropicity (ToE), first formulated and further developed by John Onimisi Obidi,[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] [36][37][38][39][40][41][42][43][44][45][46][47][48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91][92] [93] [94] [95] [96] the observer is embedded within the entropy field [as already hinted at by recent observations from Google’s Quantum Core Breakthrough Experiment on the Observer Effect]. The observer becomes an active par-ticipant in the orchestra, symphony and drama of existence in the participatory Universe[See Expository Note Below]. Collapse occurs when entropy exchange exceeds the observability threshold, governed by Obidi’s Criterion of Entropic Observability.

Expository Note: It was John Archibald Wheeler who introduced the concept of the ”participatory universe,” in which he argued that observers (or participants) are not merely passive recorders of events but actively contribute to bringing the universe into being. This notion is a key part of his participatory anthropic principle and is also linked to his famous phrase ”it from bit,” which emphasizes that information — fundamentally shaped by observation — is at the core of physical reality. But as Obidi has already explained in his Centennial Paper on Einstein and Bohr Reconciled, among other works, it is entropy that shapes information, and it is entropy that is at the core of physical reality. Thus, for ToE, it is no longer ”it from bit,” but ”bit from it.”

The Vuli–Ndlela Integral’s weighting by “classical action + entropies” has profound consequences: it imposes strict constraints on allowable quantum trajectories, replacing the unconstrained superposition of paths with an entropy-constrained existential selection principle. Interference between paths that would lead to wildly different entropy outcomes is suppressed, effectively limiting the superposition principle to those branches that respect the second law of thermodynamics. To illustrate, imagine a quantum system with two possible evolutions: Path A leads to a very low-entropy final state, Path B leads to a higher-entropy final state (perhaps because Path B entangles the system with many environmental degrees of freedom). In standard quantum theory, if both paths are dynamically allowed, they would in principle interfere.

In ToE, however, the entropy weighting in GVNI (Generalized Vuli-Ndlela Integral) biases the probability amplitude in favor of the higher entropy Path B, consistent with an “entropic arrow of time” dictated by the Vuli-Ndlela Integral Bound. If Path A’s entropy output is too low (violating entropic expectations), its contribution to ZGVNI may be exponentially damped. Thus, even at the level of virtual quantum amplitudes, entropy enforces an arrow: quantum histories that do not produce sufficient entropy are edged out by those that do. This concept is closely related to the idea of “einselection” (environment-induced superselection) in decoherence theory, wherein environmental entanglement causes certain preferred states (usually those that minimize entropy production or information leakage) to emerge. However, ToE differs by positing an intrinsic entropy field guiding this selection, rather than merely a phenomenological environment tracing-out. A concrete key equation arising in ToE is the definition of a local entropy potential associated with the quantum state. Given any wavefunction ψ(x, t) (for simplicity, non-relativistic), ToE defines an entropy density functional s(x, t) and a corresponding potential Λ(x, t).

One formulation is as follows: First, we recollect that the probability density in formal literature is given by: ρ(x, t) = |ψ(x, t)|² The entropy density functional is then given by the Shannon-like formula as earlier shown by John Obidi in Einstein and Bohr Reconciled[April 2025]: s(x, t) = −kB ρ(x, t) ln[ρ(x, t)] , where kB is Boltzmann’s constant. The corresponding entropic potential is thus defined as the functional derivative of s(x, t) with respect to ρ(x, t) [also shown by John Obidi in Einstein and Bohr Reconciled[April 2025]: Λ(x, t) = δs/δρ(x, t) = − kB[ln(ρ(x, t)) + 1] Remembering our earlier expression for the probability density, we can therefore write the above expression for the entropic potential in the general form: Λ(x, t) = − kBln|(ψ(x, t)|² + C] , where, as usual, |ψ(x, t)|² is the probability density and C is a constant offset. This Λ(x, t) is essentially a Shannon entropy per unit volume (up to constants), since −kB ln |ψ| 2 would be the contribution to information entropy at point x and time t.

References

1. Obidi, J.O. Theory of Entropicity(ToE) On Geometry and Space-Time Curvature. Encyclopedia. Available online: https://encyclopedia.pub/entry/59142 (accessed on 15 October 2025)
2. The Theory of Entropicity (ToE) On the Geometry of Existence and the Curvature of Space-Time: A Brief Overview of the Conceptual and Mathematical Evolution of the Theory of Entropicity (ToE) https://open.substack.com/pub/johnobidi/p/the-theory-of-entropicity-toe-on-fe2?r=1yk33z&utm_campaign=post&utm_medium=web&showWelcomeOnShare=false
3. The Theory of Entropicity (ToE) On the Geometry of Existence and the Curvature of Space-Time: A Brief Overview of the Conceptual and Mathematical Evolution of the Theory of Entropicity (ToE) https://medium.com/@jonimisiobidi/the-theory-of-entropicity-toe-on-the-geometry-of-existence-and-the-curvature-of-space-time-cff8e2e7f7c8
4. On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics https://open.substack.com/pub/johnobidi/p/on-the-conceptual-and-mathematical-9df?utm_source=share&utm_medium=android&r=1yk33z
5. On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics https://johnobidi.substack.com/p/on-the-conceptual-and-mathematical-9df
6. On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics https://medium.com/@jonimisiobidi/on-the-conceptual-and-mathematical-foundations-of-the-theory-of-entropicity-toe-an-alternative-20030186d0eb
7. “The Discovery of the Entropic α-Connection: How the Theory of Entropicity (ToE) Transformed…“ by John Onimisi Obidi on Medium: https://medium.com/@jonimisiobidi/the-discovery-of-the-entropic-%CE%B1-connection-how-the-theory-of-entropicity-toe-transformed-6e4e524dead7
8. Obidi, J.O. Evolutionary Introduction to the Theory of Entropicity(ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59129 (accessed on 13 October 2025)
9. An Introduction to the Theory of Entropicity (ToE): On the Evolution of its Conceptual and Mathematical Foundations (Part I) https://open.substack.com/pub/johnobidi/p/an-introduction-to-the-theory-of?utm_source=share&utm_medium=android&r=1yk33z
10. “An Introduction to the Theory of Entropicity (ToE):“ by John Onimisi Obidi on Medium: https://medium.com/@jonimisiobidi/an-introduction-to-the-theory-of-entropicity-toe-9041c28a6d3a
11. Obidi, J.O. On David Sigtermans and Obidi’s Theory of Entropicity(ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59128 (accessed on 13 October 2025)
12. Obidi, John Onimisi (2025). On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. https://doi.org/10.6084/m9.figshare.30337396.v1
13. Obidi, J.O. Conceptual and Mathematical Foundations of Theory of Entropicity(ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59127 (accessed on 13 October 2025)
14. “Sean Collins and the Mjolnir (A137) Lattice Dynamics: A Brief Introductory Note on Its Importance…“ by John Onimisi Obidi on Medium: https://medium.com/@jonimisiobidi/sean-collins-and-the-mjolnir-a137-lattice-dynamics-a-brief-introductory-note-on-its-importance-246b6749a2ac
15. Physics:Einstein’s Relativity from Obidi’s Theory of Entropicity(ToE). (2025, August 30). HandWiki, . Retrieved 12:19, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Einstein%27s_Relativity_from_Obidi%27s_Theory_of_Entropicity(ToE)&oldid=3742784
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28. Obidi, John Onimisi. Corrections to the Classical Shapiro Time Delay in General Relativity (GR) from the Entropic Force-Field Hypothesis (EFFH). Cambridge University. (11 March 2025). https://doi.org/10.33774/coe-2025-v7m6c
29. Obidi, John Onimisi. How the Generalized Entropic Expansion Equation (GEEE) Describes the Deceleration and Acceleration of the Universe in the Absence of Dark Energy. Cambridge University. (12 March 2025). https://doi.org/10.33774/coe-2025-6d843
30. Obidi, John Onimisi. The Theory of Entropicity (ToE): An Entropy-Driven Derivation of Mercury’s Perihelion Precession Beyond Einstein’s Curved Spacetime in General Relativity (GR). Cambridge University. (16 March 2025). https://doi.org/10.33774/coe-2025-g55m9
31. Obidi, John Onimisi. The Theory of Entropicity (ToE) Validates Einstein’s General Relativity (GR) Prediction for Solar Starlight Deflection via an Entropic Coupling Constant η. Cambridge University. (23 March 2025). https://doi.org/10.33774/coe-2025-1cs81
32. Obidi, John Onimisi (25 March 2025). “Attosecond Constraints on Quantum Entanglement Formation as Empirical Evidence for the Theory of Entropicity (ToE)”. Cambridge University. https://doi.org/10.33774/coe-2025-30swc
33. Obidi, John Onimisi. Einstein and Bohr Finally Reconciled on Quantum Theory: The Theory of Entropicity (ToE) as the Unifying Resolution to the Problem of Quantum Measurement and Wave Function Collapse. Cambridge University. (14 April 2025). https://doi.org/10.33774/coe-2025-vrfrx
34. Obidi, John Onimisi . “On the Discovery of New Laws of Conservation and Uncertainty, Probability and CPT-Theorem Symmetry-Breaking in the Standard Model of Particle Physics: More Revolutionary Insights from the Theory of Entropicity (ToE)”. Cambridge University. (14 June 2025). https://doi.org/10.33774/coe-2025-n4n45
35. Obidi, John Onimisi. A Critical Review of the Theory of Entropicity (ToE) on Original Contributions, Conceptual Innovations, and Pathways towards Enhanced Mathematical Rigor: An Addendum to the Discovery of New Laws of Conservation and Uncertainty. Cambridge University.(2025–06–30). https://doi.org/10.33774/coe-2025-hmk6n
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52. Correspondence Between the Theory of Entropicity(ToE) and the Idea of the Aether and the Higgs Field Mechanism in the Standard Model of Particle Physics https://open.substack.com/pub/johnobidi/p/correspondence-between-the-theory?utm_source=share&utm_medium=android&r=1yk33z
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56. The Limit of the Speed of Light © is a Consequence of [Thermodynamic] Entropy Rather Than the Geometry of Einstein’s Theory of Relativity. By John Onimisi Obidi on Medium: https://medium.com/@jonimisiobidi/the-limit-of-the-speed-of-light-c-is-a-consequence-of-thermodynamic-entropy-rather-than-the-6ee6c04aae60
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58. Physics:The Emergence of the Speed of Light in the Theory of Entropicity(ToE). (2025, September 30). HandWiki. Retrieved 06:37, September 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:The_Emergence_of_the_Speed_of_Light_in_the_Theory_of_Entropicity(ToE)&oldid=3743551
59. How Does the Theory of Entropicity(ToE) Describe Nature in Modern Physics? https://medium.com/@jonimisiobidi/how-does-the-theory-of-entropicity-toe-describe-nature-in-modern-physics-ae5739a15e7c
60. How Does the Theory of Entropicity(ToE) Describe Nature in Modern Physics? https://open.substack.com/pub/johnobidi/p/how-does-the-theory-of-entropicitytoe?utm_source=share&utm_medium=android&r=1yk33z
61. Physics:How the Theory of Entropicity(ToE) Describes Nature in Physics. (2025, October 2). HandWiki, . Retrieved 00:10, October 2, 2025 from https://handwiki.org/wiki/index.php?title=Physics:How_the_Theory_of_Entropicity(ToE)_Describes_Nature_in_Physics&oldid=3743579
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63. So, Why Do Objects or Bodies or Particles Move At All? Explained By The Theory of Entropicity(ToE) https://medium.com/@jonimisiobidi/so-why-do-objects-or-bodies-or-particles-move-at-all-2749d400a026
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67. How The Theory Of Entropicity(ToE) Explains Newton’s Laws Of Motion And Einstein’s Theory Of Spacetime Curvature https://medium.com/@jonimisiobidi/how-the-theory-of-entropicity-toe-explains-newtons-laws-of-motion-and-einstein-s-theory-of-2dbd601786a0
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69. The Theory of Entropicity(ToE) Re-interprets Newton’s Gravitation and Einstein’s Relativity Under One Unifying Principle https://open.substack.com/pub/johnobidi/p/the-theory-of-entropicitytoe-re-interprets?utm_source=share&utm_medium=android&r=1yk33z
70. The Theory of Entropicity(ToE) Re-interprets Newton’s Gravitation and Einstein’s Relativity Under One Unifying Principle https://medium.com/@jonimisiobidi/the-theory-of-entropicity-toe-re-interprets-newtons-gravitation-and-einstein-s-relativity-under-aafa8bb6ce95
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84. On the Mathematical Foundations of the Theory of Entropicity(ToE): A Qualitative Odyssey and Roadmap https://open.substack.com/pub/johnobidi/p/on-the-mathematical-foundations-of?utm_source=share&utm_medium=android&r=1yk33z
85. On the Mathematical Foundations of the Theory of Entropicity(ToE): A Qualitative Odyssey and Roadmap https://medium.com/@jonimisiobidi/on-the-mathematical-foundations-of-the-theory-of-entropicity-toe-a-qualitative-odyssey-and-aeb2f754addc
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87. On The Uniqueness of the Theory of Entropicity (ToE) With Respect to Other Competing Theories in Modern Theoretical Physics https://open.substack.com/pub/johnobidi/p/on-the-uniqueness-of-the-theory-of?utm_source=share&utm_medium=android&r=1yk33z
88. Physics:Rényi Entropy Derived from Obidi’s Theory of Entropicity(ToE). (2025, October 6). HandWiki, . Retrieved 05:56, October 6, 2025 from https://handwiki.org/wiki/index.php?title=Physics:R%C3%A9nyi_Entropy_Derived_from_Obidi%27s_Theory_of_Entropicity(ToE)&oldid=3743623
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90. The Theory of Entropicity ToE: On a New Path Toward Quantum Gravity https://open.substack.com/pub/johnobidi/p/the-theory-of-entropicity-toe-on?utm_source=share&utm_medium=android&r=1yk33z
91. Sean Collins (February, 2025). On the Theory of Mjolnir (A137) Lattice Dynamics by Sean Collins: Collected Unpublished Works and Communications with John Onimisi Obidi (Unpublished). Self-archived manuscript and materials.
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94. On the Potency of Sean Collins’ Mjolnir (A137) Lattice Dynamics Path Integral Formulation of Quantum Mechanics and Its Incorporation Into the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE) https://open.substack.com/pub/johnobidi/p/on-the-potency-of-sean-collins-mjolnir?utm_source=share&utm_medium=android&r=1yk33z
95. “On the Potency of Sean Collins’ Mjolnir (A137) Lattice Dynamics Path Integral Formulation of…“ by John Onimisi Obidi on Medium: https://medium.com/@jonimisiobidi/on-the-potency-of-sean-collins-mjolnir-a137-lattice-dynamics-path-integral-formulation-of-6ec8ac23e7ab
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