Foundational reordering of physical and informational principles

The Theory of Entropicity (ToE) establishes a systematic reordering of physical, geometrical, and informational principles by promoting entropy from a secondary, statistical descriptor to the primary field of reality. In contrast to conventional frameworks in which entropy is treated as a derived measure of disorder, unavailable energy, or informational uncertainty, the ToE posits that a single, universal entropic field underlies and generates all observable structure. Within this hierarchy, geometry, matter, and dynamics are emergent manifestations of the configuration and evolution of this underlying entropic substrate.

The central organizing idea of the hierarchy is that entropy generates geometry and matter, rather than being generated by them. The universe is therefore modeled as a stratified structure in which the entropic field occupies the foundational level, and all higher-level physical phenomena arise as derived, localized, and quantized expressions of this field.

Axiomatic hierarchy of the Theory of Entropicity (ToE)

Fundamental axiom: the entropic field as universal substrate

At the base of the hierarchy lies a single fundamental axiom: entropy, represented by a field \(S(x)\), is a universal, physical, and dynamic field that underlies all of reality. The function \(S(x)\) is defined on an appropriate manifold and assigns to each point \(x\) a value of the entropic field. This field is not a bookkeeping device for microscopic states but a genuine physical entity with its own curvature, gradients, and dynamics. All other structures—such as spacetime geometry, matter distributions, and interaction laws—are induced by the configuration and evolution of \(S(x)\).

Derived necessities of the entropic substrate

From the fundamental axiom, several necessary structural features follow. These are not independent assumptions but logical consequences of treating entropy as a universal field.

A first derived necessity is the principle of minimum distinguishability, encoded in the Obidi Curvature Invariant, given by the quantity \(\ln 2\). This invariant is interpreted as the minimal quantum of distinguishability in the entropic manifold. No new physical state can be recognized as distinct until the entropic curvature has changed by at least \(\ln 2\). In other words, the transition between distinguishable states is quantized in units of the Obidi Curvature Invariant, and this quantization constrains how the entropic field can evolve in a physically meaningful way.

A second derived necessity is the principle of dynamical curvature evolution. The entropic field evolves according to a variational principle defined by the Obidi Action. This action functional encodes the dependence of the entropic field on its gradients, curvature, and potential structure, and its variation yields field equations that determine how physical laws, spacetime structure, and matter content emerge from the underlying entropic dynamics. The Obidi Action thus plays a role analogous to that of an action in conventional field theory, but with entropy as the primary degree of freedom.

A third derived necessity is the principle of a finite rate of transformation, expressed in the No-Rush Theorem. This theorem states that physical events cannot occur instantaneously; they must await sufficient entropic maturation. In formal terms, there exists a finite upper bound on the rate at which the entropic field can reconfigure, and this bound constrains the temporal evolution of all physical processes. The No-Rush Theorem is sometimes summarized by the expression that God or Nature cannot be rushed (G/NCBR), but in technical terms it asserts that the dynamics of the entropic field impose a fundamental temporal granularity on physical transformations.

Functional hierarchy of emergence

The functional hierarchy of the ToE describes how observable physical structures arise as emergent layers built upon the entropic field. The universe is modeled as a hierarchy of localized and quantized expressions of an otherwise invisible entropic substrate.

Fundamental layer: the entropic substrate

At the most basic level lies the entropic field \(S(x)\) itself. This field possesses well-defined curvature, gradients, and dynamics. Its configuration at each point and its evolution in time encode the informational and physical content of the universe. All higher-level structures are functions of, or constraints on, this underlying entropic configuration.

Emergent geometry as entropic mapping

Spacetime geometry is interpreted as an emergent, large-scale mapping of entropic gradients. Rather than being fundamental, the smooth manifold of spacetime arises as a coarse-grained representation of the structure of \(S(x)\). Regions with different entropic configurations correspond to different effective geometrical properties, and the familiar metric structure of spacetime is induced by the entropic field. In this sense, geometry is a macroscopic encoding of the underlying entropic manifold.

Emergent matter as compactified entropy

Matter is modeled as arising from high-density, stable, and effectively compactified regions of entropy. These regions correspond to localized configurations of the entropic field that are dynamically stable and resistant to dispersion. The compactification of entropy in such regions gives rise to effective mass, energy density, and particle-like behavior. Thus, what is ordinarily described as matter is, in this framework, a particular mode of organization of the entropic substrate.

Emergent dynamics as entropic curvature and gradients

Forces and energy are interpreted as emergent manifestations of entropic curvature and entropy gradients. Gravity, in particular, is modeled as a consequence of the curvature of the entropic field and the tendency of systems to evolve along directions favored by entropic increase. Other interaction patterns can be understood as different ways in which entropy gradients constrain the motion and configuration of matter-like compactifications. In this view, dynamics is not imposed externally but arises from the internal structure of the entropic manifold.

Emergent time as entropic flow

Time is identified with the direction of the irreversible flow of entropy. It is not treated as an independent dimension but as a parameter that indexes the progression of entropic reconfigurations. The arrow of time is thus directly linked to the monotonic aspects of entropic evolution, and temporal ordering reflects the sequence of entropic states rather than an external temporal background.

Quantum behavior as synchronized entropy flow

Quantum coherence and entanglement are interpreted as phenomena arising from synchronized entropy flows between distinct regions of the entropic manifold. When regions share a coordinated entropic evolution, they exhibit correlations that, in conventional quantum theory, are described as entanglement. The ToE thus provides an entropic interpretation of quantum behavior, in which non-classical correlations are manifestations of structured, synchronized dynamics of the underlying entropic field.

The Obidi Action hierarchy

The dynamics of the entropic field are organized into a hierarchical structure of action principles, reflecting both local and global aspects of entropic evolution. This hierarchy provides a systematic way to connect infinitesimal behavior with large-scale, spectral properties of the entropic manifold.

Local Obidi Action

The Local Obidi Action (LOA) governs the infinitesimal and local behavior of the entropic field. It is constructed from entropy gradients, typically expressed as \(\nabla S\), and from an entropic potential \(V(S)\). The local action density depends on combinations such as \(\nabla_\mu S \nabla^\mu S\) and \(V(S)\), and its variation yields local field equations that describe how the entropic field responds to nearby configurations. The LOA thus captures the differential structure of the entropic field and determines its short-scale dynamics.

Spectral Obidi Action

The Spectral Obidi Action (SOA) extends the description to global and spectral aspects of the entropic field. It is formulated in terms of an operator \(\Delta\) defined by

\[ \Delta = G_{\alpha}(S) \cdot g^{-1}, \]

where \(G_{\alpha}(S)\) is a functional of the entropic field that encodes how entropy influences the effective geometry, and \(g^{-1}\) denotes the inverse of an induced metric tensor. This operator captures the way in which the entropic field shapes the underlying information geometry, including structures associated with Fisher–Rao and Fubini–Study metrics. The SOA therefore governs the spectral properties of the entropic manifold and connects the entropic field to the geometry of probability and state spaces.

Master Entropic Equation

The combination of the Local Obidi Action and the Spectral Obidi Action yields a governing field equation referred to as the Master Entropic Equation (MEE). This equation plays the role of an entropic analogue of Einstein’s Field Equations, providing a unified description of how the entropic field determines effective geometry, matter distributions, and dynamical behavior. The MEE encapsulates the hierarchical structure of the theory by linking local differential behavior with global spectral constraints.

Hierarchy of constants and limits

Within the ToE, fundamental constants are interpreted as limits and structural features of the entropic field, rather than as arbitrary parameters. This reinterpretation embeds familiar constants into the entropic hierarchy and explains their roles in terms of entropic dynamics.

Speed of light as maximum entropic propagation rate

The speed of light, usually denoted \(c\), is reinterpreted as the maximum entropic propagation rate. It represents the upper bound on the rate at which the entropic field can rearrange information and reconfigure its state. This bound constrains all physical processes, since any change in geometry, matter configuration, or interaction pattern must be mediated by the entropic field. The constant \(c\) thus acquires a direct entropic meaning as a limit on the speed of entropic reorganization.

Quantum of information and the Obidi Curvature Invariant

The quantity \(\ln 2\), identified as the Obidi Curvature Invariant, is interpreted as a quantum of information and as the minimal change in entropic curvature required for a state to be recognized as distinct. This invariant defines a lower bound on meaningful state transitions in the entropic manifold. In this way, the ToE links the quantization of information directly to the structure of the entropic field and its curvature, embedding informational discreteness into the geometry of the substrate.

Taken together, these constants and limits reinforce the central reversal of the classical view: information and entropy are fundamental, while matter and energy are emergent. The hierarchy of the ToE thus provides a coherent framework in which physical, geometrical, and informational quantities are unified as different aspects of a single entropic field.

References

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2. 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.
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16. International Journal of Current Science Research and Review (IJCSRR)
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