The Theory of Entropicity (ToE) establishes entropy not as a statistical byproduct of disorder but as the fundamental field and causal substrate of physical reality. Central to this formulation is the Obidi Action, a variational principle. By integrating the Fisher–Rao and Fubini–Study metrics through the Amari–Čencov alpha-connection formalism, ToE provides a rigorous information-geometric foundation for entropy-driven dynamics.
Analysis of John Onimisi Obidi’s Theory of Entropicity (ToE) and David Sigtermans Total Entropic Quantity (TEQ): Converging Paths Toward the Foundations of Nature and Reality
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Analysis of John Onimisi Obidi’s Theory of Entropicity (ToE) and David Sigtermans Total Entropic Quantity (TEQ): Converging Paths Toward the Foundations of Nature and Reality
Analysis of John Onimisi Obidi’s Theory of Entropicity (ToE) and David Sigtermans Total Entropic Quantity (TEQ)
Converging Paths Toward the Foundations of Nature and Reality
Introduction: Entropy‑Based Frameworks in Physics
The quest to understand the foundations of nature and reality has led to two groundbreaking entropy‑driven frameworks: David Sigtermans’ Theory of Total Entropic Quantity (TEQ) and John Onimisi Obidi’s Theory of Entropicity (ToE). While TEQ explains how physical structure emerges from curved entropy geometry, ToE advances this vision by treating entropy itself as the fundamental dynamical field that drives spacetime, matter, and information.
In this comparative overview, we explore how ToE functions as a superset of TEQ, absorbing TEQ’s core constructs — such as entropy curvature, resolution boundaries, and entropy‑weighted dynamics — into a broader entropic manifold governed by variational principles, unified metrics, and deformation parameters. By situating TEQ within its entropic Noether framework and extending entropy‑driven conservation laws, ToE not only recovers standard physics in limiting cases but also provides a meta‑theoretical foundation for unifying gravity, quantum mechanics, and information theory.
This relationship highlights the growing importance of entropy‑based cosmology and information geometry in modern theoretical physics, offering a pathway toward a deeper understanding of reality’s underlying structure.
Overview of ToE and TEQ relationship
TEQ treats physical structure as emergent from curved entropy geometry; ToE treats entropy itself as the fundamental dynamical field driving reality. In that sense, ToE generalizes TEQ’s ontology and methods, absorbing TEQ’s “entropy curvature,” “resolution boundaries,” and “entropy-weighted dynamics” as special cases within a broader entropic manifold governed by variational principles, unified metrics, and deformation parameters. ToE recovers standard physics in limits, while keeping TEQ-like constructs as localized models of entropic dynamics. Moreover, ToE explicitly analyzes and extends TEQ in its own corpus, situating TEQ inside an entropic Noether framework and entropy-driven conservation.
Core Axioms and Constructs Comparison Between ToE and TEQ
How ToE Becomes a Superset Mathematically
Entropy field and curvature
Field elevation: ToE promotes entropy to a continuous dynamical field whose gradients generate motion, gravitation, time, and information flow. TEQ’s “curved entropy geometry” is naturally interpreted as the geometry induced by this field; TEQ’s curvature is a subset of ToE’s entropic manifold constructions.
Unified metric structure and “resolution boundaries”
Metric fusion: ToE unifies Fisher–Rao (classical) and Fubini–Study (quantum) metrics through the Amari–Čencov α‑connection. TEQ’s “resolution boundaries” map to finite‑information/finite‑resolution slices in this metric family; the α parameter acts as a deformation index controlling coarse‑to‑fine entropic resolution and curvature strength, embedding TEQ’s boundary logic as one regime of ToE’s metric geometry.
Entropy‑weighted dynamics and path integrals
Variational and integral forms: ToE’s Obidi Action yields entropic geodesics and a master evolution equation; its Vuli‑Ndlela Integral is an entropy‑weighted reformulation of Feynman’s path integral that introduces irreversibility. TEQ’s “entropy‑weighted dynamics” and path‑integral derivations appear as special cases where the weight functional and boundary conditions match ToE’s integrals under appropriate α and potential choices.
Stable distinction and causality tensors
Causal structure: TEQ’s stable distinction pairs with ToE’s causal substrate: entropy gradients define causal arrows and irreversibility. ToE’s entropic Noether perspective links conservation laws to entropy‑constrained symmetries, generalizing TEQ’s information‑theoretic causal tensors within a broader conservation framework.
Scope and limits: why TEQ sits inside ToE
Limiting recoveries: ToE reproduces Einstein’s field equations as a limit and subsumes entropy‑gravity approaches, which means TEQ’s gravitational and thermodynamic constructs can be recovered within ToE’s parameter regimes and boundary conditions. This positions TEQ as a domain‑specific instantiation of ToE’s general entropic dynamics.
Meta‑theory stance: Public comparative treatments have explicitly concluded ToE functions as a broader meta‑framework under which applied entropy models like TEQ can be contextualized, reinforcing the superset claim in both conceptual and mathematical terms.
Practical Mapping from TEQ to ToE
TEQ entropy curvature → ToE entropic manifold curvature: match via α‑connection choice and entropy potential.
TEQ resolution boundaries → ToE finite‑information slices: set α and metric scales to encode boundary‑dependent dynamics.
TEQ entropy‑weighted dynamics → ToE Vuli‑Ndlela Integral: choose weighting functional consistent with TEQ’s axioms; irreversibility emerges naturally.
TEQ causal tensors → ToE entropic Noether symmetries: derive conservation relations from entropy‑constrained invariances, extending TEQ’s inference tools.
The Overarching Scope of the Theory of Entropicity (ToE)
The Theory of Entropicity is a superset of Total Entropic Quantity because it elevates entropy to a fundamental field with a unified geometric and variational structure, provides entropy‑weighted quantum dynamics with irreversibility, and recovers standard physics in limits; TEQ’s constructs — entropy curvature, resolution boundaries, and entropy‑weighted dynamics — arise as special regimes within ToE’s entropic manifold and action principles, a relationship explicitly analyzed and extended in ToE’s published work.
References
Further Resources on the Theory of Entropicity (ToE):
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