Physics:Information and Energy Redistribution in Theory of Entropicity(ToE)

Initiation of Redistribution in the Theory of Entropicity(ToE)

In the Theory of Entropicity (ToE), first formulated and developed by John Onimisi Obidi, the redistribution of information and energy in a system or interaction is not a secondary effect. It is directly initiated by the entropic field whenever a system crosses an entropic threshold. This initiation can be described through the following principles:

1. Trigger: Entropic Gradient

The fundamental driver is the existence of an entropic gradient.

• Whenever there is a difference in entropy density (Λ) between regions, the entropic field enforces a flow.
• This gradient is dynamical rather than statistical, compelling systems to move toward equilibrium by redistributing information and energy.
• In ToE, entropy acts as a field flux, analogous to how an electric field drives charge redistribution.

2. Constraint: The Entropic Time Limit (ETL)

Redistribution does not occur instantaneously.

• The ETL principle states that every interaction must "pay" an entropy cost in time.
• Redistribution begins at the smallest allowed interaction interval, preventing instantaneous adjustments.
• This enforces causality and irreversibility:

[math]\displaystyle{ \Delta t \geq t_{ETL} }[/math]

3. Mechanism: The Obidi Action and Vuli-Ndlela Integral

Mathematically, redistribution is governed by the Obidi Action and the Vuli-Ndlela Integral.

• The integral applies entropic weights that suppress impossible configurations and amplify physically consistent flows.
• Redistribution emerges as the least-constraint path in entropy space.

The generalized Vuli-Ndlela Integral is expressed as:

[math]\displaystyle{ Z_{ToE} = \int_{\mathbb{S}} \mathcal{D}[\phi] \, e^{\tfrac{i}{\hbar} S[\phi]} \, e^{-\tfrac{\mathcal{S}_G[\phi]}{k_B}} \, e^{-\tfrac{\mathcal{S}_{irr}[\phi]}{\hbar_{eff}}} }[/math]

4. Local Initiation: Self-Referential Entropy (SRE)

At the subsystem level (particles, fields, or minds in psychentropy), redistribution initiates through Self-Referential Entropy (SRE).

• When SRE deviates from the global entropic field, the system is compelled to adjust.
• This forces energy and information to flow until alignment is restored.

5. Physical Picture of Entropic Redistribution of Information and Energy

In summary:

• Redistribution begins with a mismatch in entropic balance (an entropic gradient).
• The entropic field enforces correction within the finite ETL interval.
• Redistribution is the manifestation of energy and information flow until entropic consistency is achieved.

Summary Statements

In ToE:

• Trigger: Entropic gradient.
• Constraint: Entropic time limit (ETL).
• Mechanism: Obidi Action and Vuli-Ndlela Integral.
• Local initiation: Self-Referential Entropy (SRE).

Thus, redistribution is not probabilistic but a deterministic demand of the entropic field for balance.

Origin of Redistribution in the Theory of Entropicity (ToE) — Further Insights

A central question in the Theory of Entropicity (ToE) is: what actually initiates the redistribution of information and energy in a system? It cannot be said that entropy itself starts the process, because that would risk circular reasoning. Instead, entropy is the law of redistribution, but its origin must be identified separately.

1. Distinguishing Entropy from Its Source

In ToE, entropy acts as the field constraint that governs how information and energy must flow.

• In gravity, spacetime curvature governs motion, but the origin of curvature is mass–energy.
• In electromagnetism, the electric field governs charge motion, but the origin is the presence of electric charge.
• Likewise, in ToE, the source of redistribution must be specified independently of entropy itself.

2. The Origin: Boundary Asymmetry

The actual origin of redistribution is asymmetry in boundary constraints.

• When a system possesses unequal or misaligned constraints, such as differences in entropy density, energy levels, or microstates, an entropic potential difference arises.
• This asymmetry compels redistribution, which then unfolds under the governance of entropy.
• Thus, it is not entropy that starts redistribution, but the existence of unequal conditions (finite, zero, infinite boundaries, or mismatched states).

3. Physical Picture

Redistribution can be understood through direct analogy:

• Electricity: charges move not because the electric field wills them, but because a potential difference exists.
• Gravity: matter falls not because gravity initiates motion, but because mass–energy curves spacetime, leaving no alternative trajectory.
• ToE: redistribution of energy and information begins not because "entropy wants it," but because constraint asymmetry creates a disequilibrium that must be resolved.

4. Candidate Origins in ToE Language

Several specific formulations of this origin can be given in ToE:

1. Constraint asymmetry: misaligned finite (F), infinite (I), or zero (Z) boundaries.
2. Irreversibility injection: every interaction is subject to the entropic time limit (ETL), which introduces unavoidable time-asymmetry.
3. Self-Referential Entropy (SRE) mismatch: subsystems compare their entropy with the global field; mismatches initiate redistribution automatically.

5. Analogy Table

Field	Governing Law	Source/Origin
Gravity	Spacetime curvature	Mass–energy
Electromagnetism	Maxwell’s equations	Electric charge
Entropicity (ToE)	Entropic field constraints	Boundary asymmetry / irreversibility

6. Boundary Conditions as Triggers

Every physical system exists within boundaries — finite (F), zero (Z), or infinite (I).

• If all boundaries are perfectly symmetric and balanced, no net flow occurs.
• The moment differences appear — e.g., a finite boundary next to an infinite one, or a subsystem with fewer microstates adjacent to one with more — an entropic potential difference exists.

This mismatch is not static: it creates a "pressure" to transform one boundary state into another, analogous to how a voltage difference drives charge flow.

Example: A hot object (finite high entropy density) in contact with a cold one (finite low entropy density). The boundary asymmetry initiates heat flow. Without the asymmetry, nothing starts.

7. Irreversibility as a Catalyst

Even with a boundary difference, if interactions were perfectly reversible, redistribution could in principle oscillate back and forth without any net change.

What makes redistribution start and persist is irreversibility:

• Every interaction is subject to the Entropic Time Limit (ETL), which forbids instant reversibility.
• The ETL injects an arrow of time: once redistribution starts, it cannot "go back" in exactly the same way.
• This small but unavoidable irreversibility ensures that boundary mismatches cannot remain dormant — they must initiate flows.

8. How the Initiation Works in Practice

The initiation of redistribution can be described as a three-step mechanism:

1.Constraint asymmetry arises: [math]\displaystyle{ \Delta \Lambda = \Lambda_1 - \Lambda_2 \neq 0 }[/math] (difference in entropy density, boundary type, or microstate count).

2.Irreversibility enforces action: The ETL forbids stasis; even if balanced forces exist, they cannot hold perfectly due to time’s arrow.

3.Entropy governs redistribution: Once triggered, entropy’s field law dictates the exact flow of information and energy until balance is restored.

9. Physical Picture of the Entropic Mechanism of Redistribution of Information and Energy

The mechanism can be understood by analogy with other fields:

• In gravity, a mass creates curvature asymmetry → particles move.
• In electromagnetism, a charge creates potential difference → currents flow.
• In ToE, a boundary constraint asymmetry creates entropic imbalance → information and energy redistribute, with irreversibility ensuring it actually happens.

10. Compact Statement for the Redistribution Mechanism

Differences in boundary conditions create entropic imbalances (like a pressure or potential), and irreversibility (ETL) ensures these imbalances cannot remain static. This dual mechanism is what actually initiates redistribution; entropy then provides the law of how the redistribution proceeds.

11. How Entropy Governs Redistribution

A natural question arises in the Theory of Entropicity (ToE): how does entropy know how to redistribute energy and information once redistribution is initiated? The answer lies in treating entropy as a fundamental field governed by equations of motion, not as a passive statistical measure.

1. Entropy as a Field with Governing Laws

Entropy is a field analogous to the gravitational and electromagnetic fields.

• In gravity, motion is governed by Einstein’s field equations.
• In electromagnetism, charges are governed by Maxwell’s equations.
• In ToE, redistribution is governed by the Obidi Action and its path-integral formulation, the Vuli-Ndlela Integral.

Thus, entropy "knows" how to redistribute because the mathematical laws of the entropic field strictly determine the permitted flows.

2. Entropy Density Functional

Redistribution follows gradients of the entropy density functional:

[math]\displaystyle{ \Lambda(\phi) = \frac{k_B c^3}{\hbar G} A(\phi) + \frac{dS}{dt} }[/math]

• If [math]\displaystyle{ \Delta \Lambda \neq 0 }[/math], redistribution occurs.
• The direction of redistribution is set by the sign of [math]\displaystyle{ \Delta \Lambda }[/math].
• The magnitude of redistribution is determined by the steepness of the gradient.

Just as water flows downhill due to gravitational potential, energy and information flow "downhill" along entropy gradients.

3. Irreversibility as the Selector of Path

Even when multiple flows are mathematically possible, irreversibility fixes the outcome.

• The Entropic Time Limit (ETL) forbids exact reversibility.
• ETL enforces a unique, causal, and time-directed trajectory for redistribution.

This injects the arrow of time into every redistribution event.

4. Self-Referential Entropy (SRE)

At the subsystem level, Self-Referential Entropy (SRE) provides local guidance.

• Each subsystem compares its internal entropy against the global entropic field.
• Redistribution proceeds to minimize this mismatch.
• Local SRE checks and the global Obidi Action together ensure consistent redistribution at all scales.

5. Physical Analogy to Gravity and Electromagnetism

• In gravity, spacetime curvature dictates how matter moves.
• In electromagnetism, Maxwell’s equations dictate how charges respond.
• In ToE, the entropic field equations dictate how energy and information redistribute.

Entropy governs redistribution by enforcing lawful flows along entropy gradients, always constrained by ETL and locally guided by SRE.

6. Key Statement on ToE Redistribution

Entropy does not "choose" how to redistribute. Redistribution pathways are dictated by the entropic field equations derived from the Obidi Action. Flows follow entropy gradients, irreversibility (ETL) fixes the arrow of redistribution, and Self-Referential Entropy (SRE) provides local initiation, ensuring the process is both lawful and directional.

12. Entropic Geodesics for the Redistribution of Information and Energy

In the Theory of Entropicity (ToE), a central question arises: what physical path is dictated by the entropic field equation? Just as matter follows trajectories in spacetime or charges follow field lines, ToE requires its own governing principle of motion.

1. The Analogy with Other Fields

• In gravity, matter follows spacetime geodesics dictated by the Einstein field equations.
• In electromagnetism, charges and currents follow trajectories determined by Maxwell’s equations.
• In ToE, energy and information follow entropic geodesics, dictated by the entropic field equation derived from the Obidi Action.

Thus, entropic geodesics are the analog of gravitational geodesics or electromagnetic field lines.

2. Definition of Entropic Geodesics

The physical path in ToE is defined as the trajectory of least entropic resistance. This is the path that extremizes the entropic action functional:

[math]\displaystyle{ \delta \int \Lambda(x) \, dt = 0, }[/math]

where [math]\displaystyle{ \Lambda(x) }[/math] is the entropy density functional, typically expressed as:

[math]\displaystyle{ \Lambda(\phi) = \frac{k_B c^3}{\hbar G} A(\phi) + \frac{dS}{dt} }[/math]

3. Rules of Path Selection

The entropic geodesic emerges from three principles:

1. Gradient flow: trajectories align with entropy gradients [math]\displaystyle{ \Delta \Lambda }[/math].
2. Irreversibility constraint: the Entropic Time Limit (ETL) forbids oscillatory or reversible solutions, enforcing a time-oriented flow.
3. Least-constraint principle: among all irreversible flows, the system follows the path that minimizes entropic expenditure.

4. Physical Interpretation

• In gravity, the geodesic minimizes the spacetime interval.
• In electromagnetism, currents follow field lines consistent with Maxwell’s equations.
• In ToE, entropic geodesics are the irreversible least-constraint trajectories along which energy and information redistribute under the guidance of entropy.

These paths embody both the global constraints of the Obidi Action and the local checks of Self-Referential Entropy (SRE).

5. Analogy Table on Physical Trajectory

Framework	Governing Equation	Physical Path
Gravity	Einstein field equations	Spacetime geodesic
Electromagnetism	Maxwell’s equations	Current/field line trajectory
Entropicity (ToE)	Entropic field equation (Obidi Action, Vuli-Ndlela Integral)	Entropic geodesic (least entropic resistance path)

6. Key Takeaway Insight

In the Theory of Entropicity, the entropic field equation dictates that systems follow entropic geodesics — trajectories of least entropic resistance. These paths are enforced by entropy gradients, fixed by the irreversibility of ETL, and locally guided by Self-Referential Entropy.

13. Balancing vs Increasing Entropy in ToE

A natural question arises: if entropy always increases according to the Second Law of Thermodynamics, how can redistribution in the Theory of Entropicity (ToE) be said to "balance" entropy? The resolution lies in distinguishing between local balance and global increase.

1. The Paradox

• Classical thermodynamics: entropy always increases in a closed system.
• ToE: redistribution balances entropy across boundaries.
• The puzzle: how can entropy be "balanced" if it must always increase?

2. The Resolution in ToE

In ToE, balance does not mean reduction of entropy, but redistribution of entropy density.

• Global law: total entropy of the closed system always increases.
• Local law: redistribution reduces entropy gradients between subsystems or boundaries.

Thus, entropy increases overall, but its distribution becomes balanced locally.

3. Analogy in Classical Physics

• Heat flow: When heat flows from hot to cold, local temperature differences vanish (balance), but total entropy of the system increases irreversibly.
• Entropic redistribution: Local entropy densities equalize, but the process itself generates additional entropy, preserving the global increase.

4. The Mechanism

Redistribution operates by:

1. Eliminating asymmetries in entropy density (finite vs infinite, high vs low).
2. Driving systems toward a uniform entropic configuration.
3. Doing so irreversibly under the Entropic Time Limit (ETL).

Formally, the change in total entropy can be written as:

[math]\displaystyle{ \Delta S_{total} = \Delta S_{redistribution} + \Delta S_{generation} \gt 0 }[/math]

• [math]\displaystyle{ \Delta S_{redistribution} }[/math]: reduction of local gradients (balancing).
• [math]\displaystyle{ \Delta S_{generation} }[/math]: entropy produced by the irreversibility of the redistribution process.

5. Physical Parallel

• In gravity: geodesics balance curvature by directing matter flow, but the global mass–energy remains.
• In electromagnetism: charge flow balances potentials, but energy is dissipated irreversibly.
• In ToE: redistribution balances entropy locally (removes gradients), while total entropy always increases globally.

6. Noteworthy Insight

In ToE, redistribution does not stop entropy from increasing. Instead, it balances entropy locally by reducing asymmetries in entropy density, while the total entropy of the closed system continues to increase irreversibly. The entropic field thus smooths local imbalances even as global entropy rises without bound.

14. Related Research on Entropic Geodesics

The proposal in the Theory of Entropicity(ToE) that physical trajectories are governed by entropic geodesics—paths of least entropic resistance defined by an action principle—is novel in its own right, but there are precedents in related fields that touch similar themes, though not precisely in the way it has been ambitiously formulated in the Theory of Entropicity(ToE).

1. Entropic Dynamics (Cafaro and collaborators)

Carlo Cafaro and collaborators developed Entropic Dynamics (ED), where system evolution is derived from an entropy-based action principle. In this framework, trajectories correspond to geodesics on probability manifolds defined by entropy-like metrics.

• These geodesics are not in physical spacetime, but in statistical state space.
• This shares conceptual parallels with ToE in that both describe motion as geodesic evolution constrained by entropy.

2. Minimum Entropy Production Paths (Quantum Information Geometry)

Gassner, Cafaro, Ali, Alsing and others have studied geodesic evolution in quantum state space using information geometry.

• In their results, quantum state evolution can follow minimum entropy production paths.
• These paths represent geodesics that minimize entropy production, conceptually akin to the ToE principle of least entropic resistance.

3. Entropic Density Functional Theory (eDFT)

Ali Yousefi and colleagues proposed an Entropic Density Functional Theory (eDFT).

• Here, entropy-based variational principles are used to derive density functionals.
• While not explicitly defining physical trajectories, these works use entropy functionals in a variational framework, paralleling the entropic action of ToE.

4. Entropic Gravity (Verlinde, Jacobson)

Erik Verlinde and Ted Jacobson have independently proposed that gravity emerges as an entropic phenomenon.

• In Verlinde’s approach, motion arises from entropy gradients on holographic screens.
• Jacobson showed that Einstein’s field equations can be derived from the thermodynamics of horizons.
• Although less formal in terms of trajectories, this perspective resonates with ToE’s claim that entropy fields dictate motion.

5. Comparative Summary of the Literature

Researcher / Framework	Core Idea	Relation to ToE Entropic Geodesics
Carlo Cafaro (Entropic Dynamics — ED)	Geodesic motion on entropy-defined statistical manifolds	Parallels in action principle; statistical vs. physical entropy field
Gassner, Cafaro, Ali, Alsing (Quantum IG)	Minimum entropy production paths in quantum state space	Conceptual parallel to least entropic resistance trajectories
Ali Yousefi (eDFT)	Entropy-based density functionals	Reinforces variational use of entropy; no explicit trajectories
Verlinde, Jacobson (Entropic Gravity)	Gravity as entropic force from gradients	Philosophical overlap; lacks entropic geodesic formalism

6. On the Distinction of the Formulation of the Theory of Entropicity(ToE)

While the Theory of Entropicity is unique in defining physical entropic geodesics via the Obidi Action and entropy density functional, related efforts in Entropic Dynamics, quantum information geometry, entropic density functionals, and entropic gravity demonstrate converging interest in entropy as a guiding principle of motion. ToE distinguishes itself by explicitly formulating an entropic field equation that dictates real physical trajectories in spacetime, not just in probability or informational manifolds. In this way, the Theory of Entropicity(ToE) provides an explicitly bold imperative on the foundations of physics rooted in full field theoretic entropy.

15. Philosophical Significance

The Theory of Entropicity(ToE) offers a perspective that is both rigorous and profound for theoretical physics to contemplate. By reframing entropy from a statistical measure into a fundamental field principle, ToE establishes a structural parallel with established field theories.

1. Source–Law Separation

ToE clarifies that:

• Constraint asymmetry and irreversibility act as the source of the entropic field.
• Entropy field equations (the Obidi Action and the Vuli-Ndlela Integral) provide the governing law of redistribution.

This mirrors how mass–energy sources gravity with Einstein’s equations as its law, and how charge sources electromagnetism with Maxwell’s equations as its law. The removal of circularity gives entropy a precise role in physics, as well as a structural rigor comparable to existing field theories.

2. Entropic Geodesics

ToE introduces the concept of entropic geodesics—trajectories of least entropic resistance.

• These define the physical paths along which energy, matter, and information redistribute.
• They extend the idea of geodesics beyond spacetime curvature into the domain of entropy itself.
• This offers a unified geometric framework linking thermodynamics, information theory, and relativity.

This makes ToE a candidate for a geometric entropy-based physics, akin to how GR geometrized gravity.

3. Balance vs. Increase Paradox Resolved

ToE resolves the paradox of entropy balancing and entropy increasing.

• Globally: entropy always increases in line with the Second Law of Thermodynamics.
• Locally: redistribution balances entropy by reducing gradients and asymmetries.

This dual interpretation by the Theory of Entropicity(ToE) thus boldly transforms entropy from a purely statistical law into a dynamic field principle.

This dual view — local smoothing with global growth — reframes how we interpret the Second Law, embedding it into a field theory rather than a mere statistical rule.

4. Bridging Existing Approaches

ToE synthesizes and extends existing entropic frameworks:

• Verlinde and Jacobson: gravity as entropic gradients.
• Cafaro: entropic dynamics and geodesics in information space.
• Quantum information geometry: minimum entropy production paths.

ToE therefore distinguishes itself by proposing an explicit entropic field equation that governs real physical trajectories in spacetime.

Thus, ToE offers a unifying lens through which many disparate entropic approaches can be connected, but without reducing itself to any of them.

5. A New Physics Frontier

By elevating entropy to the status of a fundamental field:

• ToE suggests that the true driver of the universe is not only force, curvature, or probability, but entropy flow.
• It introduces a new class of laws where irreversibility is not emergent, but primary.
• It positions entropy alongside mass, charge, and curvature as a foundation for unifying physics.

Hence, the Theory of Entropicity(ToE) provides a new way to ask: what if the universe’s true driver is not force, curvature, or probability, but entropy flow?

This otherwise annihilating insight is profound, because it opens a new frontier where thermodynamics, relativity, and quantum mechanics are not patched together, but unified under entropy.

6. Challenges from the Theory of Entropicity(ToE)

The Theory of Entropicity challenges physics and physicists to reconsider entropy as more than disorder or probability.

ToE reframes entropy from a statistical measure into a fundamental field principle. It not only parallels but also extends the structure of Einstein’s and Maxwell’s field theories, offering a potentially unifying foundation for physics.

By proposing entropic geodesics, a clear source–law separation, and a reconciliation of local balance with global increase, ToE offers a new unifying principle that theoretical physics must ponder as a possible foundation for its future.

16. Entropic Clock Postulate (ECP)

“Every tick of a clock, every interval it traverses, is an entropic event in nature. Time is registered not by ideal instants but by finite increments of entropy. Therefore, entropy must be a field that dictates and governs reality and all interactions.”

1. Statement of the Postulate

• ECP: A clock tick is a finite entropic event and the sequence of ticks is a record of entropy flow through the system.
• Timekeeping is thus operationally equivalent to counting entropic events; no tick occurs without a nonzero entropic increment.

2. Field Interpretation

• Entropy is treated as a field whose local density and flux govern interactions and measurement outcomes.
• The entropic field supplies the lawful dynamics (via the Obidi Action / Vuli-Ndlela Integral), while constraint asymmetries and irreversibility act as sources that initiate flows.

3. Entropic Interval and Minimal Tick

• An observed time step corresponds to a finite entropic increment:

[math]\displaystyle{ \Delta t \;\propto\; \Delta \Xi \,,\quad \Delta \Xi \gt 0, }[/math]

where [math]\displaystyle{ \Xi }[/math] is a cumulative entropy functional tied to the entropic field.

• There exists a nonzero Entropic Time Limit (ETL) such that no interaction (and thus no tick) can occur faster than:

[math]\displaystyle{ \Delta t \ge t_{\mathrm{ETL}} \gt 0 }[/math]

4. Entropic Distance (Operational Notion)

• The “interval distance” between ticks reflects the traversed entropic distance along an entropic geodesic:
• Larger local entropy gradients yield shorter tick spacing (faster ticking).
• Smaller gradients yield wider spacing (slower ticking).
• Conceptually: clocks are entropy flux meters; their rates encode the local entropic field.

5. Consequences and Intuition Pumps

1. Arrow of time: Each tick records an irreversible step (no exact reversal beyond ETL).
2. Synchronization: Co-located ideal clocks agree because they sample the same entropic field; differing environments (constraints/gradients) induce rate differences.
3. Dynamics: Systems (energy, information) follow entropic geodesics—paths of least entropic resistance—so measured time tracks progress along these paths.

6. Testable Implications (Programmatic)

• Clock rates should correlate with controlled changes in entropy flow (e.g., engineered constraint asymmetries or informational load).
• Devices with different internal dissipation profiles (but identical nominal frequency standards) may show systematic rate shifts when embedded in distinct entropic environments.

7. Conclusion on Space and Time as Entropic Events in Nature

A tick is an entropic event; an interval is an entropic distance. Because every act of measurement (including timekeeping) requires finite entropy flow, entropy cannot merely be statistical bookkeeping. It must be a field that governs interactions and the unfolding of reality.

17. Zero-Entropy Limit Means: No Time, No Geometry

Claim of The Theory of Entropicity(ToE): If there is no entropy (no entropic field, no gradients, no irreversibility), then there is no time and no geometry—hence no spacetime.

1. Why This Follows in ToE

1. No ticks, no time: In ToE, a clock tick is an entropic event (ECP). With zero entropy, no finite entropic increments occur; clocks do not tick; operational time is undefined.
2. No irreversibility, no ordering: The Entropic Time Limit (ETL) supplies the arrow of time. With zero entropy, ETL collapses and there is no directed sequence of events.
3. No field, no path: Entropic geodesics (paths of least entropic resistance) require an entropic field. With no field, there are no physically selected trajectories—dynamics are undefined.
4. No metric, no geometry: In ToE the effective geometry is induced by entropic structure (densities/fluxes). With no structure (no gradients), the metric becomes trivial/degenerate; geometry does not emerge.

2. Interpretation of Space and Time in Terms of the Theory of Entropicity(ToE)

• Time is the bookkeeping of entropic events; remove events and time evaporates as an observable.
• Geometry encodes how flows organize; remove the field that organizes flows and geometry loses meaning.
• Thus, spacetime is an emergent bookkeeping of the entropic field’s lawful, irreversible organization.

3. Boundary Note (Idealization)

The strict zero-entropy state is a limiting idealization. Any physically realizable system carries nonzero entropy (or fluctuations), reinstating ticks, ordering, paths, and metric structure of reality.

4. Closure on Entropic Space and Time

No entropy ⇒ no irreversibility, no ticks, no trajectories, no metric. Therefore, no time and no geometry (no spacetime) in the ToE sense.

17. Summary of the Insights on ToE's Redistribution of Information and Energy

In the Theory of Entropicity:

• Entropy is not the origin but the law of redistribution.
• The trigger is always the presence of a constraint asymmetry (finite vs infinite, reversible vs irreversible, SRE mismatches).
• Once asymmetry exists, entropy governs how energy and information are redistributed until entropic balance is restored.

Therefore, the source of the entropic field can be physically pointed to as boundary asymmetry and irreversibility within the system, not entropy itself.

That is to say:

It is not entropy itself that initiates redistribution, but constraint asymmetry—differences in boundary conditions and irreversibility—which entropy then acts upon to redistribute energy and information.

We hence note the following:

• Constraint asymmetry (boundary differences, irreversibility, SRE mismatch) = the source (the origin trigger).

• Entropy field = the law that governs the redistribution once triggered.

• This origin of redistribution helps to remove circularity and makes ToE structurally analogous to the great physical field theories:
  • Mass is the source of gravity, spacetime curvature is the law.
  • Charge is the source of electromagnetism, Maxwell’s equations are the law.
  • Constraint asymmetry is the source of the entropic field, entropy flow laws (Obidi Action, Vuli-Ndlela Integral) are the law.

Let us conclude our program so far by casting our thoughts in the form of a universal principle:

Obidi’s Principle of Entropic Origin (OPEO):

It is not entropy itself that initiates redistribution, but constraint asymmetry — differences in boundary conditions and irreversibility — which entropy then acts upon to redistribute energy and information.