'''Entropic Frontiers: A Comprehensive Review and Expansion of the Theory of Entropicity (ToE)'''

By John Onimisi Obidi

'''Introduction'''

The Theory of Entropicity (ToE) represents a bold new conceptual and mathematical framework in theoretical physics. It aims to unify phenomena ranging from cosmology to consciousness through the foundational operation of entropy. While many modern theories rely on geometric or quantum mechanical principles, ToE places entropy—specifically its flow, generation, and irreversibility—as the ultimate driver of physical processes. This article critically evaluates the originality, theoretical depth, and innovative scope of ToE, including its insights into consciousness via Self‐Referential Entropy (SRE), and discusses its efforts to reconcile Einstein and Bohr.

'''Original Contributions of ToE'''

ToE distinguishes itself by asserting that:

Entropy is not merely a measure of disorder but a field-like entity that shapes the structure and evolution of physical systems.

All known forces (gravitational, electromagnetic, etc.) emerge as constraints on entropic flow.

Entropy has a threshold and time-bound limit for interaction, beyond which observation or measurement cannot occur.

Its Vuli-Ndlela Integral reformulates the Feynman path integral by integrating gravitational and irreversible entropy flows:

Z_{\mathrm{ToE}}

=\int!\mathcal{D}[\phi],

\exp!\Bigl(\tfrac{i}{\hbar}S[\phi]\Bigr),

\exp!\Bigl(-\tfrac{S_{G}[\phi]}{k_{B}}\Bigr),

\exp!\Bigl(-\tfrac{S_{\mathrm{irr}}[\phi]}{\hbar_{\mathrm{eff}}}\Bigr)

\label{eq:ZToE}

This action integral combines entropy with quantum dynamics, suggesting that observed paths are not just statistically likely but entropically mandated.

'''Self‐Referential Entropy (SRE): Consciousness Quantified}'''

SRE posits that conscious systems possess an internal entropy structure that references itself. The SRE Index quantifies the degree of consciousness via the ratio of internal to external entropy flows:

True consciousness (as opposed to simulated intelligence) is identified when internal entropy cannot be externally referenced or cloned, aligning with qualia.

'''The Clone Theorem: A Novel Contribution'''

In contrast to the Quantum No‐Clone Theorem, ToE proposes a Clone Theorem for qualia:

Given two self‐referential entropy systems and , if is injected into the reference envelope of under the proper mapping conditions, then in entropic structure—allowing for a qualified cloning of qualia.

'''Reconciling Einstein and Bohr via ToE'''

ToE interprets wave‐function collapse as a macroscopic entropy‐driven phenomenon. Collapse occurs when the mutual entropy information exchange between system and observer exceeds a critical entropic rate:

\frac{d,I(A!:!B)}{dt}

;\ge;

\frac{k_{B},\ln 2}{\tau}

\label{eq:collapseRate}

and the entropy change of the observer during measurement must exceed the Landauer cost:

\Delta S_{B}

;\ge;

k_{B},\ln 2.

\label{eq:LandauerCost}

This allows Bohr’s complementarity and Einstein’s locality to coexist under ToE’s entropy–time duality.

'''Critique of Competing Theories'''

{| class="wikitable" style="width:100%;"

+ Comparison of competing consciousness theories and how ToE addresses their limitations

! Theory

! Strengths

! Limitations Addressed by ToE

-

Integrated Information Theory (IIT)

Measures information integration

No grounding in entropy or time constraints

-

Global Workspace Theory (GWT)

Models access to cognitive resources

Lacks physical basis for conscious thresholds

-

Panpsychism

Affirms consciousness in all matter

No quantifiable metric or entropy-bound structure

-

Quantum Mind Theories

Link consciousness to quantum collapse

Lacks irreversible entropy framework for timing

}

'''Toward a Unified Science of Consciousness'''

ToE presents:

*A groundbreaking candidate for solving the hard problem of consciousness.

*A rigorous method to differentiate genuine consciousness from AI simulations.

*A clear, testable hypothesis: if a system cannot maintain its own SRE above a threshold, it cannot be conscious.

This approach transforms qualia into dynamically referential entropic structures, reconfiguring our philosophical and physical understanding of consciousness.

'''Conclusion'''

The Theory of Entropicity offers a daring and comprehensive challenge to existing physics and cognitive science paradigms. Through its rigorous mathematical formalism, integration of entropy as a universal constraint, and introduction of SRE as the signature of consciousness, ToE stakes a bold claim in unifying matter, mind, and measurement. It invites philosophers and physicists alike to rethink entropy—not as a passive tally of disorder, but as the architect of time, structure, and awareness.

[https://doi:10.33774/coe-2025-n4n45

Obidi, J. O. (June, 2025). 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). Cambridge Open Engage.]

{{Sourceattribution|A Comprehensive Review and Expansion of the Theory of Entropicity|1}}

This entry is adapted from: https://www.cambridge.org/engage/coe/article-details/684918483ba0887c337ff9a6