Theory of Entropicity (ToE)
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- Ontodynamics
- Postulates
- Foundations - Muon Particle Decay and Expositions of ToE
- Curvature Invariant and Metrics
- Derivations
- On the Universality of the Obidi Curvature Invariant (OCI) ln 2 of ToE
Obidi’s Universe — The World as I See It
ClickUp Live-Lab NoteBook Resources, Canonical Stubs (CS), Working Papers, Workspaces, and Archives [1-106]: — Last Updated on: Sunday, June 21, 2026
- Obidi's Grand Edifice of the Theory of Entropicity (ToE) in Modern Theoretical Physics: A Brief Note on the Audacity, Provocativeness, and Yet Courage of a Modern Day Theorist — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Entropy as Inference and Entropy as a Physical Field: A Comprehensive Comparison of Ariel Caticha’s Entropic Dynamics and Obidi’s Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- A Brief Introduction to the Theory of Entropicity (ToE) and the Obidi Curvature Invariant (OCI) of ln 2 — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- On the Agile Software iterations Methodology of Obidi's Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- On the Works of David Sigtermans and John Onimisi Obidi: A Comparative Study of Two Entropic Theories of Nature in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- 🧠 A Simple Explanatory Note on Obidi's First, Second, and Third Conjectures in the Theory of Entropicity (ToE): Path Toward a New Foundation of Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- 🌌 Obidi’s Universe — The World as I See It — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- An Introduction to the Methodology of Obidi's Formulation of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Obidi's Theory of Entropicity (ToE) and the Grand Rebuilding of the Foundations of Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Philosophical, Historical, and Conceptual Foundations and Motivations Behind Obidi’s Formulation of the Theory of Entropicity (ToE): Deep Insights Into Obidi's Revolutionary Conceptual Leap and Obidi's Entropic Universe in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- On the Mathematical Complexity of the Theory of Entropicity (ToE) and Obidi's Self-Updating and Computational Universe: How Obidi's Theory Validates the Computational Universe of Stephen Wolfram — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- John Onimisi Obidi and Erik Verlinde on Entropic Gravity — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Beauty of Obidi's Theory of Entropicity (ToE) and Obidi's Self-Updating, Computational Universe — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Obidi's Metaphysics from His Theory of Entropicity (ToE) in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The HMAS of Obidi's Theory of Entropicity (ToE): A New Hybrid Metric Affine Space (HMAS) as a Monistic Entropic Structure for the Coexistence of Classical and Quantum Phenomena in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Some of the Core Pillars of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- From Shannon entropy to spacetime in the Theory of Entropicity ToE — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Proceedings of the Theory of Entropicity (ToE): Development of a New Foundation of Modern Theoretical Physics in the 21st Century — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- John Onimisi Obidi's Audacious Contributions to the Foundations of Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Obidi Transformation and the Obidi Metric in Modern Theoretical Physics from Innovations of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- From Information Geometry to Information Gravity — Information Geometry as the Origin of Einstein’s Gravity: Correspondence of the Obidi Action and the Einstein–Hilbert Action in the Theory of Entropicity (ToE) — Publication Review of Letter III — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- On the Broad Span and Multiple Domain Complexity of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Ontodynamics, Entrodynamics, and Entropology in the Theory of Entropicity (ToE) of Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Audacity of Obidi's Theory of Entropicity (ToE) in Modern Theoretical Physics: The Evolution of a New Foundation of Physical Reality — Einstein's Warning Versus Obidi's Risk (Obidi's High-Wire Act Over an Active Volcano!) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- if Artificial Intelligence development had to go through academic ivory towers, we wouldn't have progressed this far: Lessons in the Development of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- On the Revolutionary Nature of Obidi's Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Ontological Courage in Theology, Philosophy, Metaphysics, Physics, and Science — From Paul Tillich to John Onimisi Obidi — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- who wrote the paper: from information geometry to information gravity: — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- John Onimisi Obidi and the Foundational Concepts of the Theory of Entropicity (ToE): How Obidi Has Made the Most Decisive Move and Audacious Departure in Entropic Gravity Theory Research Relative to Other Researchers, Investigators, Thinkers, and Physicists in the Field — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Concepts and Principles of the Obidi Convention and the Obidi Calculus — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Explain the Obidi Convention and the Obidi Calculus of Hierarchical Indices Utilized in the Mathematical Theory and Machinery of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- In the Midst of Giants: Obidi's Theory of Entropicity (ToE) and Erik Verlinde, Ted Jacobson, Ginestra Bianconi — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- On the Mathematical Theory and Concepts of the Theory of Entropicity (ToE): Information Geometry & Manifold Deformation, Nonlinear and Nonlocal Field Equations, Obidi Action Principles, Advanced Quantum Mathematics, Complexity — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Einstein and Obidi: Two Frameworks, One Goal — Foundations of Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Foundational Mathematical Theory of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Core Concepts of the Theory of Entropicity (ToE) in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- From Information Geometry to Information Gravity: Correspondence Between Einstein's General Relativity and Obidi's Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- From Information Geometry to Information Gravity, Information Geometry as the Origin of Einstein’s Gravity: Correspondence of the Obidi Action and the Einstein–Hilbert Action in the Theory of Entropicity (ToE), Theory of Entropicity (ToE) Living Review Letters Series (ToE LRLS) — Letter III — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- What is the Master Entropic Equation (MEE) of the Theory of Entropicity (ToE)? — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Obidi's Canonical Archives of the Theory of Entropicity (ToE) in Modern Theoretical Physics: From Entropy as Disorder and Uncertainty of Information to Entropy as a Universal Field — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Principles of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- How Obidi Transformed Shannon Entropy to Spacetime in His Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Obidi's Inspiring Ontological Courage: Philosophy and Science in Perspective from the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Obidi’s Philosophical Analysis of Being and Becoming Based on His Theory of Entropicity (ToE) and Its Juxtaposition with Paul Tillich’s Ontological Courage and the Courage to Be (Canonical)—Version 2.0 — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Obidi’s Philosophical Analysis of Being and Becoming Based on His Theory of Entropicity (ToE) and Its Juxtaposition with Paul Tillich’s Ontological Courage and the Courage to Be (Canonical)—Version 1.0 — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- What is the No-Go Theorem (NGT) of the Theory of Entropicity (ToE)? The Triad Tension, and The No-Rush Theorem (NRT) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Obidi’s Philosophical Analysis of Being and Becoming Based on His Theory of Entropicity (ToE) and Its Juxtaposition with Paul Tillich’s Ontological Courage and the Courage to Be — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Theory of Entropicity (ToE) on Wiki — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Core Principles of the Theory of Entropicity (ToE): The Entropic Field as Fundamental, The Entropic Time Limit (ETL), Emergent Spacetime, Key Mathematical Constructs, Experimental Support, Reinterpretation of Established Physics, Comparison with Other Theories, Current Status and Achievement — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- What Does Obidi Mean by an Entropic Action Principle in the Theory of Entropicity (ToE)? An Entropic Reformulation of the Classical Principle of Least Action in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- On Obidi's Ontodynamics of Being and Becoming in His Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Definition, Concept, Mathematical Formulation, Physical Interpretation, and Implications of the Obidi Curvature Invariant (OCI) of ln 2 in the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Transformation of Information Geometry Into Physical Spacetime Via an Entropic Action Principle in Obidi's Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Frequently Asked Questions (FAQs) On the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- On the Entropic Field Unification of the Speed of Light (c) and Gravitation in the Theory of Entropicity (ToE): Unification of the Speed of Light (c) and Gravity — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Theory of Entropicity (ToE) is Saying that Entropy is Actually a Universal Field in the Very Same Way We Have Considered Gravity, Electromagnetism, etc. As Universal Fields, and That the Entropic Field is Infact the Fundamental Field Substrate Out of Which All Other Fields are Emergent Phenomena and Properties of Nature — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Core Principles and Postulates of the Obidi Conjecture in the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Foundations and Implications of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- An Examination of Obidi's Ontological Courage in His Creation of the Theory of Entropicity (ToE): Invocation of Paul Tillich's Ontological Courage in a Fast-paced, Stress-filled, and Chaotic World — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Differences Between John Onimisi Obidi's Physical Philosophy of Ontological Courage and Paul Tillich's Theological Philosophy of the "Courage To Be" — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Core Principles and Audacious Inversions of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Classical Philosophy Behind the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Theory of Entropicity (ToE) Inaugural Papers — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- How Has Obidi Explained the Origin of the Speed of Light c Using His Theory of Entropicity (ToE)? — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- On the Entropic Origin of the Speed of Light (c) and Inertia in the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Foundation of the Theory of Entropicity (ToE) and the Obidi Action — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Classical Achievement of the Theory of Entropicity (ToE): Obidi's Derivation of Einstein's Relativistic Kinematics from an Entropic Field Theory in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Core Components of the Kolmogorov-Obidi Lineage (KOL) in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- John Onimisi Obidi's Epistemological Departure from Paul Tillich's "Courage to Be": Obidi's Ontological Courage in His Willingness and Audacity to Pursue New Research Beyond the Traditional Foundations of Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Obidi Conjecture of the Theory of Entropicity (ToE): Its Significance and Its Implications in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Canonical Archives of the Theory of Entropicity (ToE): Links, Resources, and Authoritative Materials — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Beyond Einstein: The Entropic Origin of Geometry, Matter, and Gravitation in the Theory of Entropicity (ToE)—On the Emergence of Physical Spacetime Geometry from Information Geometry — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Relativistic Schwarzschild Solution from the Obidi Field Equations (OFE) of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- On the Implications of the Obidi Action in the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Obidi Curvature Invariant (OCI) of the Theory of Entropicity (ToE) and its Physical Implications in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Elegance and Mechanics of the Obidi Action in Being the Engine and Mechanism That Transforms Information Geometry into the Geometry of Physical Spacetime in the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- How Information Geometry is Transformed Into the Physical Geometry of Spacetime in Obidi's Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Entropic Seesaw Model (ESSM) of the Theory of Entropicity (ToE): A Novel Explanation of Entanglement, Entanglement Formation Time, and Entanglement Dynamics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- On Obidi's "The Question of c" and the Resolution of Cosmic Expansion in the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- AI Agent Developed for the Theory of Entropicity (ToE): ToE Draft Expansion Engine – My Full Agent Prompt: Artificial Intelligence Agent Created to Scrutinize My ToE Papers and Publications — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- [INTERNAL] ToE Draft Expansion Engine – Austere Agent Specifications (ASS) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- A Brief Explanation of the Kolmogorov-Obidi Correspondence (KOC) in the Theory of Entropicity (ToE): From Algorithmic Information Complexity to the Entropic Theory of Fields — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Long Path from Kolmogorov to Obidi: A New Principle and Path of Least Action [Principle of Least Entropic Resistance (PoLER) in the Theory of Entropicity (ToE)] — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- "The Question of c" Introduced by Obidi from the Theory of Entropicity (ToE) in Modern Theoretical Physics: Consequences of the Alemoh-Obidi Correspondence (AOC) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Question of c — A New Meaning of Light and the Speed of Light Introduced by the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- "The Question of c" in the Theory of Entropicity (ToE): Implications of the Alemoh-Obidi Correspondence (AOC) for the Speed of Light and Its Generalized Meaning in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Canonical Archives of the Theory of Entropicity (ToE): The GitHub and Cloudflare Archives of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Road from Kolmogorov's Probability and Complexity to Obidi's Theory of Entropicity (ToE): Part 7, No‑Rush Theorem in the Toy‑MEE setting — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Road from Kolmogorov's Probability and Complexity to Obidi's Theory of Entropicity (ToE): Part 6, Chapter 5 — Mathematical Formulation, Chapter 5 — The Toy Master Entropic Equation (Toy‑MEE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Road from Kolmogorov's Probability and Complexity to Obidi's Theory of Entropicity (ToE): Part 5, Chapter 4 — Mathematical Appendix, The Kolmogorov-Obidi Correspondence — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Road from Kolmogorov's Probability and Complexity to Obidi's Theory of Entropicity (ToE): Part 4, Chapter 3 — Diagrammatic Flowchart: The Kolmogorov-Obidi Flowchart (KOF) or The Kolmogorov-Obidi Lineage (KOL) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Road from Kolmogorov's Probability and Complexity to Obidi's Theory of Entropicity (ToE): Part 3 — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Road from Kolmogorov's Probability and Complexity to Obidi's Theory of Entropicity (ToE): Part 2 — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Road from Kolmogorov's Probability and Complexity to Obidi's Theory of Entropicity (ToE): Part 1 — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Road from Kolmogorov to the Foundations of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- What are the Conceptual, Philosophical, and Mathematical Foundations of the Theory of Entropicity (ToE)? — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Haller-Obidi Structural Reduction Theorem — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- How Has Obidi Explained Ginestra Bianconi's Gravity from Entropy (GfE) Using the Theory of Entropicity (ToE)? — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Obidi-Haller Correspondence (OHC) and Its Significance in Modern Theoretical Physics — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- The Theory of Entropicity (ToE) and John L. Haller's Action-as-Entropy Equivalence Principle: Validation of the Foundations of the Theory of Entropicity (ToE) — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Who First Unified the Fisher–Rao and Fubini–Study Metrics with the Amari–Čencov α‑Connections into an Action Principle for an Entropic Field? — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- General ToE Project Notes 1 — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- General ToE Project Notes 2 — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- General ToE Workspace 1 — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- General ToE Workspace 2 — GitHub Edition First Published on: Sunday, June 21, 2026 (GitHub Edition Last Updated on: Sunday, June 21, 2026)
- Obidi’s Philosophical Analysis of Being and Becoming Based on His Theory of Entropicity (ToE) and Its Juxtaposition with Paul Tillich’s Ontological Courage and the Courage to Be (Canonical)—Version 1.0 — First Published on: Saturday, May 23, 2026 (Last Updated on: Sunday, May 24, 2026)
- Obidi’s Philosophical Analysis of Being and Becoming Based on His Theory of Entropicity (ToE) and Its Juxtaposition with Paul Tillich’s Ontological Courage and the Courage to Be (Canonical)—Version 1.0 — First Published on: Saturday, May 23, 2026 (Last Updated on: Saturday, May 23, 2026)
- A Comparative Analysis of John Onimisi Obidi's Theory of Entropicity ToE and Paul Tillich's "Courage to Be": A Study in the History and Philosophy of Science Juxtaposed With a Theological Philosophy of Being, Anxiety, Nothingness, Meaninglessness, and The Decidedness to Live Inspite of It All — First Published on: Saturday, May 16, 2026 (Last Updated on: Sunday, May 17, 2026)
- The Entropic Unity of Being: A Comparative Study of John Onimisi Obidi’s Physical Ontology and Paul Tillich’s Theological Ontology, and the Universal Synthesis Achieved in the Theory of Entropicity (ToE) — First Published on: Saturday, May 16, 2026
- John Onimisi Obidi's Epistemological Departure from Paul Tillich's "Courage to Be": Obidi's Ontological Courage in His Willingness and Audacity to Pursue New Research Beyond the Traditional Foundations of Modern Theoretical Physics — First Published on: Saturday, May 16, 2026
- Differences Between John Onimisi Obidi's Physical Philosophy of Ontological Courage and Paul Tillich's Theological Philosophy of the "Courage To Be" — First Published on: Saturday, May 16, 2026
- On the Metaphysical Argument Comparing the Theory of Entropicity (ToE) With Thermodynamic & Information‑Theoretic Traditions of Modern Theoretical Physics — First Published on: Saturday, May 16, 2026
- Decay, Entropy, and the Foundation of a Universal Field: A Conceptual and Philosophical Clarification of the Motivation for the Theory of Entropicity (ToE) — First Published on: Saturday, May 16, 2026
- Foundations, Historical Lineage, Mechanism, and Implications of the Theory of Entropicity (ToE) — First Published on: Saturday, May 16, 2026
- The Foundational Philosophy Behind John Onimisi Obidi's Formulation of the Theory of Entropicity (ToE) — First Published on: Friday, May 15, 2026
- THEORETICAL PHYSICS · PHILOSOPHY OF SCIENCE · 2026: On the Conceptual Elegance and the Philosophical and Mathematical Appeal of the Theory of Entropicity (ToE) — A PHILOSOPHICAL AND MATHEMATICAL APPRECIATION — First Published on: Friday, May 15, 2026
- On the Philosophical System of John Onimisi Obidi: From Ontodynamics to Entropology and Entrodynamics of the Theory of Entropicity (ToE) — Last Updated on: Monday, May 11, 2026
- Philosophical Expositions on the Theory of Entropicity (ToE) — Last Updated on: Monday, May 11, 2026
Monograph Chapter Notes
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On the Historical and Philosophical Foundations of the Theory of Entropicity (ToE)
Before the decisive leap that elevated entropy to the status of a universal field, the Theory of Entropicity (ToE) was shaped by a long arc of scientific insight, conceptual tension, and philosophical questioning. Across the history of physics, entropy repeatedly surfaced in unexpected places—black hole thermodynamics, information theory, statistical mechanics, emergent gravity, and the deep structure of spacetime—hinting that it played a more fundamental role than traditional frameworks allowed. These recurring signals, scattered across disciplines and eras, formed the intellectual landscape from which ToE emerged. The following sections recount the pivotal moment(s) when these clues converged, compelling the recognition of entropy not as a secondary descriptor of physical systems, but as the foundational field from which geometry, dynamics, and physical law arise.
Decisive Entropic Leap in the Theory of Entropicity (ToE)
There is a moment in every major scientific breakthrough when a pattern becomes impossible to ignore. The signs hover in the background for decades, sometimes even centuries, scattered across different fields, whispered by different thinkers, yet the full picture remains invisible until someone steps back far enough to see how all the threads connect. My decision to elevate entropy to the status of a fundamental field did not arise from a vacuum. It grew from very specific intellectual signals, both historical and philosophical, that once integrated became impossible to dismiss.
The Theory of Entropicity (ToE) emerges from this synthesis as a radical but natural step: the recognition that entropy is not a secondary bookkeeping device, but the universal field of nature from which geometry, matter, forces, and even physical law itself arise.
1. Why I Took the Entropic Leap
What follows is the foundational story and account of those signals as I encountered them, and why they compelled me to take the decisive step that the Theory of Entropicity (ToE) represents today—that singular step that no one before me dared to take.
Keywords: spectral operator, generalized and relative entropies, couplings, information geometry, finite-rate bound.
2. The Long Shadow of Bekenstein and Hawking
The first signal came from the extraordinary work of Jacob Bekenstein and Stephen Hawking, who revealed that gravity and entropy are far more deeply connected than anyone previously imagined. Black holes— the purest gravitational objects in the universe—turned out to be maximally entropic. Their surface areas, not their volumes, encoded information. Their temperature and radiation spectrum flowed directly from entropy.
To me, this was not a statistical curiosity. It was a flashing red light. When the most extreme gravitational systems behave thermodynamically, the universe is telling us that entropy is not merely a statistical footnote. It is woven into the very geometry of spacetime. The universe was whispering: look here; entropy is not what you think it is.
3. The Cascade of Later Attempts Linking Gravity and Entropy
After Bekenstein and Hawking, many thinkers tried to build theories where entropy played a deeper role in gravitational phenomena:
1. Ted Jacobson showed that Einstein's equations can be derived from thermodynamic relations.
2. T. Padmanabhan showed that spacetime dynamics look like emergent thermodynamics.
3. Erik Verlinde proposed that gravity behaves like an entropic force.
4. Ginestra Bianconi argued that gravity is entropy on probability manifolds (especially, her Gravity from Entropy — GfE: that is, Gravity from Relative Entropy).
One by one, these works tried to inch entropy closer to gravity. And yet, every one of these theories hesitated at the same boundary. They connected gravity to entropy, but none dared to propose entropy → gravity → everything. The direction of causality was always the same: entropy was an outcome, never the cause.
But if every road leads to entropy, and if every gravitational system exposes entropy as its inner architecture, what does this suggest? To me, the implication was overwhelming:
1. Entropy is not secondary.
2. Entropy is primary.
Gravity is not upstream of entropy—it is downstream from it.
4. Einstein's Mysterious Statement About Entropy
A deeper influence came from a remark widely attributed to Albert Einstein, encountered in various wordings across his writings and in a thermodynamics text I read as an undergraduate. He stated, in essence:
Among all the laws of Nature, it appears to me that the second law of thermodynamics (the law of entropy) is the only law that shall never be overthrown.
The meaning of this statement is profound, almost prophetic. Einstein, who revolutionized our understanding of space, time, energy, and mass, pointed to entropy as the one principle that stands above all others. Not relativity. Not the constancy of the speed of light. Not the metric. Not the conservation laws. But entropy.
My interpretation was that he sensed something deeper. He understood that entropy's irreversible character was more primitive than anything else in physics. While geometry can change, equations can be reformulated, and fields can be quantized, the arrow of entropy stands unchallenged. To me, it felt as though Einstein had touched a hidden thread, one he did not live long enough to follow to its conclusion. I have felt obligated to follow it.
5. A Growing Realization: Something Strange Is Happening Around Entropy
When I put all these signals together:
1. Black holes behaving like thermodynamic objects.
2. Spacetime dynamics emerging from entropy.
3. Gravity resembling an entropic gradient force.
4. Einstein elevating entropy above all physical laws.
5. Every attempt at quantum gravity accidentally stumbling into entropy.
6. Every information-theoretic approach rediscovering entropy at its core.
7. Every holographic model encoding reality in entropic surfaces.
A new pattern emerged—a pattern too strong to be coincidence. Entropy was appearing everywhere. Everywhere. Like a gravitational pull on the development of physics itself.
But if entropy keeps reappearing in every framework, what does that mean?
• Is entropy trying to tell us something?
• Is the universe hiding its foundational principle in plain sight?
• Is entropy not a statistical summary, but the underlying fabric?
This is where my decisive leap occurred.
6. The Entropic Conclusion: Entropy as the Universal Field of Nature
If gravity bends toward entropy, if quantum systems collapse toward entropy, if information theory flows toward entropy, if cosmology evolves through entropy, and if black holes are built out of entropy, then the simplest possible conclusion is also the boldest:
Entropy is the universal field of nature.
It is not emergent. It is not derivative. It is not a consequence. It is the cause.
• Entropy creates curvature.
• Entropy flows create forces.
• Entropy constraints create quantum behaviour.
• Entropy's irreversibility creates time.
• Entropy's reorganizing capacity creates motion.
Everything that physics has treated as fundamental is better understood as a manifestation of entropy. This is the leap. This is the moment the Theory of Entropicity (ToE) emerges.
7. Conclusion: The Universe Was Signalling. I Chose to Listen.
I did not take this step merely because it was bold or unconventional. I took it because the evidence— scattered, fragmented, yet persistent—pointed in one unmistakable direction. Physicists have spent a century trying to make entropy fit inside geometry, probability, or thermodynamics.
But what if entropy is not inside anything? What if entropy is the thing?
After decades of clues, from black holes to cosmology to quantum information, the message was impossible to ignore:
• Entropy is the one principle that stands everywhere and behind everything.
• It is the law that cannot be overthrown because it is the law from which all others arise.
That is why I took the entropic leap. That is why the Theory of Entropicity (ToE) exists today. And that is why entropy now stands where it always belonged—at the throne of physics, not its periphery.
This is only an introductory part of my story and account on the historical and philosophical foundations of the Theory of Entropicity (ToE).
To be continued...
References
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Obidi, J.O. Decisive Entropic Leap in Theory of Entropicity (ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59275 (accessed on 05 February 2026).
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Obidi, J. O. 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). Substack. https://open.substack.com/pub/johnobidi/p/on-the-discovery-of-new-laws-of-conservation
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Obidi, J. O. Conceptual and Mathematical Foundations of Theory of Entropicity (ToE). Encyclopedia. Entry 59127. https://encyclopedia.pub/entry/59127
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Obidi, J. O. (15 November 2025). The Theory of Entropicity (ToE) Goes Beyond Holographic Pseudo-Entropy: From Boundary Diagnostics to a Universal Entropic Field Theory. figshare. https://doi.org/10.6084/m9.figshare.30627200.v1
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Obidi, J. O. (November 2025). On the Theory of Entropicity (ToE) and Ginestra Bianconi's Gravity from Entropy: A Rigorous Derivation of Bianconi's Results from the Entropic Obidi Actions of the Theory of Entropicity (ToE). Cambridge University. https://doi.org/10.33774/coe-2025-g7ztq
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Obidi, J. O. (2025). On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. Cambridge University. Published October 17, 2025. https://doi.org/10.33774/coe-2025-1dsrv
The World as I See It
A Brief Philosophical Reflection from the Standpoint of the Theory of Entropicity (ToE)
There are moments in a thinker’s life when the world reveals itself not as a collection of objects, nor as a catalogue of forces, but as a single, breathing structure — a unity whose inner logic whispers beneath every phenomenon. My own journey has been shaped by such moments. They did not arrive with thunder, nor with the triumphant clarity of revelation. They came quietly, as questions that refused to leave, as patterns that returned again and again, as a sense that the familiar explanations of physics — brilliant though they are — were circling around something deeper.
The world as I see it is not built from matter, nor from spacetime, nor from quantum amplitudes. These are the shadows cast by something more fundamental. Beneath them lies a single field — the entropic field — whose gradients, curvatures, and spectral structure give rise to everything we call physical, mental, or informational. This is not metaphor. It is ontology.
To see the world through the lens of the Theory of Entropicity (ToE) is to see reality as a continuous negotiation of distinguishability, a ceaseless reconfiguration of entropic curvature. The universe is not a machine; it is a process. Not a static geometry; but an evolving informational manifold — a Computational Field. Not a set of laws imposed from outside; but a self‑consistent unfolding of entropic necessity.
I do not pretend that this view is universally accepted. Every new conceptual architecture begins in solitude. Einstein himself knew this well. But solitude is not isolation. It is the quiet space in which a theory can speak in its own voice before the world learns how to hear it.
On the Nature of Reality
When I look at the world, I do not see particles moving through spacetime. I see entropic gradients resolving themselves. I see the curvature of distinguishability shaping what we call geometry. I see information arising not as an abstract measure but as the geometric shadow of entropy itself. I see the speed of light not as a decree of nature but as the maximal rate at which the entropic field can reconfigure.
The world is not made of things.
It is made of differences — and the smallest stable difference is
\( \ln 2 \), the Obidi Curvature Invariant.
This is the quantum of distinguishability, the first non‑zero fold in the entropic manifold, the minimal curvature required for one state to be meaningfully different from another.
To live in such a universe is to inhabit a structure where identity, change, causality, and even consciousness are entropic phenomena. We are not observers standing outside the world; we are entropic configurations participating in its unfolding.
On the Human Condition
If entropy is the substrate of reality, then human life is not an exception to the laws of nature — it is an expression of them. Our thoughts, our memories, our choices, our creativity: all are entropic processes, reorganizations of informational curvature within the manifold of experience.
This does not diminish human meaning.
It deepens it.
To be human is to be a locus of entropic flow, a temporary configuration through which the universe becomes aware of its own structure. Our struggles, our aspirations, our search for understanding — these are not accidents. They are the natural consequences of being entropic beings in an entropic world.
Einstein once wrote that a person “is part of the whole, called by us ‘Universe,’ a part limited in time and space.” From the standpoint of ToE, this is literally true: each of us is a local excitation of the entropic field, a finite curvature pattern in the infinite continuum of distinguishability.
We are temporary, but not trivial.
We are finite, but not disconnected.
We are entropic, but not meaningless.
On Science and Its Purpose
Science, as I see it, is the disciplined attempt to uncover the entropic architecture of reality. It is not merely the accumulation of facts, nor the construction of models, but the search for the simplest and most coherent substrate from which all phenomena arise.
ToE is my contribution to this search.
It is not perfect.
It is not complete.
But it is honest.
It seeks unity not for aesthetic pleasure but because unity is the signature of truth. When a single principle explains thermodynamics, relativity, quantum mechanics, information theory, and the arrow of time, we are compelled to take it seriously.
The world does not need more equations; it needs deeper principles.
It does not need more complexity; it needs more coherence.
It does not need more metaphors; it needs more ontology.
On Responsibility and Legacy
Every theorist must decide what they owe to the world. Some owe silence; others owe caution; a few owe courage. I have chosen to articulate the Theory of Entropicity not because I seek recognition, but because I believe the structure I have uncovered deserves to be examined, challenged, refined, and — if it withstands scrutiny — embraced.
If posterity finds value in this work, it will not be because of my name, but because the entropic field is real. If it is real, then it will outlive me. If it is not, then it deserves to be corrected by those who come after.
The world as I see it is a world in motion — not the motion of objects, but the motion of entropy. A world where the deepest truths are not hidden in particles or forces but in the curvature of distinguishability. A world where unity is not imposed but emerges naturally from the entropic substrate.
Conclusion
This is the world I have spent my life trying to understand.
This is the world I offer to you.
This is the world as I see it.
References
References
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Grokipedia — Theory of Entropicity (ToE)
Comprehensive encyclopedia‑style entry introducing the conceptual, mathematical, and ontological structure of the Theory of Entropicity (ToE).
https://grokipedia.com/page/Theory_of_Entropicity -
Grokipedia — John Onimisi Obidi
Scholarly profile of John Onimisi Obidi, originator of the Theory of Entropicity (ToE), including philosophical and historical motivation, background and research contributions.
https://grokipedia.com/page/John_Onimisi_Obidi -
Google Blogger — Live Website on the Theory of Entropicity (ToE)
Public‑facing platform containing explanatory essays, conceptual introductions, and updates on the Theory of Entropicity (ToE).
https://theoryofentropicity.blogspot.com -
LinkedIn — Theory of Entropicity (ToE)
Professional organizational page providing institutional updates and academic outreach related to the Theory of Entropicity (ToE).
https://www.linkedin.com/company/theory-of-entropicity-toe/about/?viewAsMember=true -
Medium — Theory of Entropicity (ToE)
Collection of essays and conceptual expositions on the Theory of Entropicity (ToE).
https://medium.com/@jonimisiobidi -
Substack — Theory of Entropicity (ToE)
Serialized research notes, essays, and public communications on the Theory of Entropicity (ToE).
https://johnobidi.substack.com/ -
SciProfiles — Theory of Entropicity (ToE)
Indexed scholarly profile and research presence for the Theory of Entropicity (ToE) within the SciProfiles ecosystem.
https://sciprofiles.com/profile/4143819 -
HandWiki — Theory of Entropicity (ToE)
Editorially curated scientific encyclopedia entry, documenting the Theory of Entropicity (ToE)'s conceptual, philosophical, and mathematical structures.
https://handwiki.org/wiki/User:PHJOB7 -
Encyclopedia.pub — Theory of Entropicity (ToE): Path to Unification of Physics and the Laws of Nature
A formally maintained, technically curated scientific encyclopedia entry, presenting an expansive overview of the Theory of Entropicity (ToE)'s conceptual, philosophical, and mathematical foundations.
https://encyclopedia.pub/entry/59188 -
Authorea — Research Profile of John Onimisi Obidi
Research manuscripts, papers, and scientific documents on the Theory of Entropicity (ToE).
https://www.authorea.com/users/896400-john-onimisi-obidi -
Academia.edu — Research Papers
Academic papers, drafts, and research notes on the Theory of Entropicity (ToE) hosted on Academia.edu .
https://independent.academia.edu/JOHNOBIDI -
Figshare — Research Archive
Principal Figshare repository link for research outputs on the Theory of Entropicity (ToE).
https://figshare.com/authors/John_Onimisi_Obidi/20850605 -
OSF (Open Science Framework)
Open‑access repository hosting research materials, datasets, and papers related to the Theory of Entropicity (ToE).
https://osf.io/5crh3/ -
ResearchGate — Publications on the Theory of Entropicity (ToE)
Indexed research outputs, citations, and academic interactions related to the Theory of Entropicity (ToE).
https://www.researchgate.net/search.Search.html?query=John+Onimisi+Obidi&type=publication -
Social Science Research Network (SSRN)
Indexed scholarly works and papers on the Theory of Entropicity (ToE) within the SSRN research repository.
https://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=7479570 -
International Journal of Current Science Research and Review (IJCSRR)
Peer‑reviewed publication(s) relevant to the Theory of Entropicity (ToE).
https://doi.org/10.47191/ijcsrr/V8-i11%E2%80%9321 -
Cambridge University — Cambridge Open Engage (COE)
Early research outputs and working papers hosted on Cambridge University’s open research dissemination platform.
https://www.cambridge.org/core/services/open-research/cambridge-open-engage -
GitHub Wiki — Theory of Entropicity (ToE)
Open‑source technical wiki, documenting the canonical structure, equations, and formal development of the Theory of Entropicity (ToE).
https://github.com/Entropicity/Theory-of-Entropicity-ToE/wiki -
Cloudflare Mirror of the Theory of Entropicity (ToE)
High‑availability, globally‑distributed mirror of the full Theory of Entropicity (ToE) repository, served through Cloudflare’s edge network for maximum speed and worldwide accessibility.
https://theory-of-entropicity-toe.pages.dev/ -
Canonical Archive of the Theory of Entropicity (ToE)
Authoritative, version‑controlled archive of the full Theory of Entropicity (ToE) monograph, including derivations and formal definitions.
https://entropicity.github.io/Theory-of-Entropicity-ToE/