Entropy as Field vs. Entropy as Information: A Comparative Analysis of Obidi’s Theory of Entropicity (ToE) and Adami’s Information‑Theoretic Framework

Abstract

John Onimisi Obidi’s Theory of Entropicity (ToE) proposes that entropy is not a statistical descriptor but a fundamental ontic field that generates spacetime, matter, motion, and physical law. In contrast, Christoph Adami — a leading figure in information theory, artificial life, and quantum information — consistently treats entropy as an epistemic measure of uncertainty, grounded in Shannon information and statistical mechanics. This paper examines the conceptual, mathematical, and ontological differences between these two frameworks, evaluates whether Adami’s thesis offers a “better” description of physical reality, and argues that the two theories address different layers of reality. Adami’s work is fully consistent with mainstream physics and information theory, while Obidi’s ToE proposes a deeper ontological foundation that reinterprets the very nature of entropy, causality, and spacetime. The question is not which theory is “better,” but which level of description is more fundamental.

1. Introduction

Entropy is one of the most universal concepts in science. It appears in:

- thermodynamics  

- statistical mechanics  

- information theory  

- quantum mechanics  

- black hole physics  

- cosmology  

- complexity science  

Yet despite its ubiquity, entropy has historically been treated as a derived quantity, not a fundamental one.

Two modern thinkers approach entropy from radically different directions:

1. John Onimisi Obidi (2025–2026)

Proposes the Theory of Entropicity (ToE), in which entropy is a continuous ontic field \( S(x) \) with its own action, field equations, and causal structure.

2. Christoph Adami (1990s–2026)

A leading researcher in information theory, artificial life, and quantum information, whose work consistently treats entropy as an informational and statistical measure of uncertainty, correlation, or complexity.

These two views are not merely different — they represent two different ontologies.

This paper compares them and addresses the central question:

> Is Adami’s information‑theoretic entropy a better description of physical reality than Obidi’s entropic field?

2. Christoph Adami’s Entropy: An Information‑Theoretic Framework

Chris Adami’s work spans:

- quantum information (e.g., negative quantum entropy)  

- artificial life and digital evolution  

- complexity and biological information  

- information flow in neural and biological networks  

- quantum uncertainty  

His publications emphasize entropy as:

- a measure of uncertainty  

- a property of probability distributions  

- a tool for analyzing information flow  

- a descriptor of complexity  

Examples from Adami's work:

- “On the Origin of Quantum Uncertainty” (2020) treats entropy as an information‑theoretic quantity tied to quantum states.  

- “Emergence of Functional Information from Multivariate Correlations” (2022) frames entropy as a measure of informational structure in biological systems.  

- His quantum information work with Nicolas Cerf (1997) formalizes negative entropy as an informational concept.

2.1 Ontological Status of Entropy in Adami’s Work

In Adami’s worldview:

- entropy is epistemic, not ontic  

- entropy measures uncertainty, not physical substance  

- entropy is derived, not fundamental  

- entropy does not generate spacetime or physical law  

- entropy has no field equations or action principle  

This aligns with mainstream physics.

3. Obidi’s Theory of Entropicity (ToE): Entropy as a Fundamental Field

Obidi’s ToE proposes a radically different ontology:

3.1 Entropy as Ontic Field

Entropy is a real, continuous field \( S(x) \) that:

- generates spacetime  

- shapes geometry  

- defines causality  

- governs motion  

- produces physical law  

3.2 The Obidi Action

The Obidi Action integrates:

- information geometry  

- α‑connections  

- spectral operators  

- generalized entropies  

- causal constraints  

It is the first action principle built entirely from entropic quantities.

3.3 The Master Entropic Equation (MEE)

Analogous to Einstein’s Field Equations, the MEE governs:

- entropic curvature  

- entropic flow  

- emergent geometry  

- causal structure  

3.4 Ontodynamics

Obidi’s philosophical system interprets existence as entropic becoming:

- time = entropic directionality  

- identity = entropic pattern stability  

- causality = entropic update rate  

- being = entropic motion  

This is a metaphysical framework absent in Adami’s work.

4. Points of Conflict Between Adami and ToE

| Concept | Adami | Obidi (ToE) |

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

| Nature of Entropy | Epistemic measure of uncertainty | Ontic physical field |

| Role of Entropy | Descriptive | Generative |

| Mathematical Status | Statistical quantity | Field with action and dynamics |

| Relation to Spacetime | None | Spacetime emerges from entropy |

| Relation to Physics | Analytical tool | Substrate of physical law |

| Ontology | Information‑theoretic | Entropic‑field metaphysics |

Adami’s framework is fully compatible with mainstream physics.  

ToE proposes a new ontology that goes beyond mainstream physics.

5. Is Adami’s Thesis a Better Description of Physical Reality?

This is the central question.

5.1 If the question is: “Which theory matches current mainstream physics?”

Adami’s thesis is better aligned with the current scientific consensus.

Mainstream physics treats entropy as:

- statistical  

- informational  

- emergent  

- epistemic  

Adami’s work fits perfectly within this paradigm.

5.2 If the question is: “Which theory is more fundamental?”

Obidi’s ToE proposes a deeper ontological foundation.

ToE explains:

- why entropy appears everywhere  

- why spacetime emerges  

- why causality has a maximum rate  

- why physical laws have their form  

- why information and geometry are linked  

Adami’s framework does not attempt to answer these questions.

5.3 If the question is: “Which theory is more mathematically complete?”

Adami’s framework is mature and widely used.  

ToE is new but offers a unified variational structure that Adami’s does not.

5.4 If the question is: “Which theory is more revolutionary?”

ToE is the more radical and generative theory.

It proposes:

- a new field  

- a new action  

- a new ontology  

- a new interpretation of spacetime  

- a new causal structure  

Adami’s work does not challenge the foundations of physics.

6. Conclusion: Two Theories, Two Levels of Reality

Adami’s thesis is:

- consistent  

- powerful  

- widely accepted  

- empirically grounded  

- mathematically mature  

But it is not a theory of fundamental reality.  

It is a theory of information about reality.

Obidi’s Theory of Entropicity is:

- ontological  

- foundational  

- generative  

- unifying  

- paradigm‑shifting  

It is not “better” or “worse” — it is deeper.

Adami describes how information behaves.  

Obidi describes what reality is made of.

These are not competing theories.  

They are different layers of the same universe, where one is much deeper and fundamental than the other.