Entropicity, Neutrino Mixing, and the PMNS Matrix: A New Perspective on Neutrino Oscillations and Symmetries Based on New Insights from the Theory of Entropicity(ToE)

When Entropy Enters the Neutrino: Rethinking the PMNS Matrix Through Obidi’s Theory of Entropicity (ToE)

Abstract

This paper develops a novel interpretation of neutrino mixing and oscillation phenomena by embedding them within the Theory of Entropicity (ToE), a framework in which entropy is promoted from a statistical descriptor to a fundamental dynamical entity. Within this paradigm, entropy is treated as an active field capable of coupling to quantum systems, inducing irreversible dynamics, modifying symmetry principles, and reshaping conservation laws. Applying ToE to neutrino physics, the work proposes that entropy-driven mechanisms can naturally generate or influence the structure of the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) mixing matrix, offering a new physical rationale for large leptonic mixing angles and CP violation.

The paper introduces a reinterpretation of CPT symmetry in the presence of intrinsic entropy flow, formulates an Entropic Noether’s theorem linking symmetry breaking to entropy production, and proposes a thermodynamic uncertainty principle that establishes a fundamental entropic time limit for quantum processes. These concepts are applied to neutrino oscillations, mass hierarchy, CP violation, and the Dirac–Majorana question. The analysis further explores how entropic effects may induce decoherence, modify oscillation probabilities, generate environment-dependent CP phases, and lead to subtle violations of conventional conservation laws. Finally, the paper discusses phenomenological consequences for current and future experiments, including T2K, NOνA, DUNE, and JUNO, outlining potential observational signatures that could distinguish entropic dynamics from Standard Model expectations.

Long Overview: Entropy, Neutrinos, and the Foundations of Mixing

1. Motivation: Why Revisit Neutrino Physics Through Entropy?

Neutrinos occupy a unique position in fundamental physics. They are extraordinarily abundant, weakly interacting, and deeply connected to unresolved questions about mass generation, CP violation, and the matter–antimatter asymmetry of the universe. While the PMNS matrix successfully parametrizes neutrino mixing and oscillations, it does not explain why the mixing angles take their observed values, nor why CP violation appears to be potentially large in the lepton sector.

This paper argues that these unresolved features may be signaling physics that lies beyond conventional quantum field theory—specifically, physics associated with irreversibility, information flow, and entropy. The Theory of Entropicity (ToE) provides the conceptual and mathematical setting for this investigation by treating entropy as a real, dynamical participant in fundamental processes rather than as a passive statistical measure.

2. Core Idea of the Theory of Entropicity

At the heart of ToE is the assertion that entropy possesses field-like properties: it can flow, couple to matter, break symmetries, and influence dynamics at the most fundamental level. In this view, entropy is associated with a field $𝑆 (𝑥)$ and an entropy current $𝑆^{𝜇}$ , allowing irreversibility to be encoded directly into the equations of motion.

This has profound implications. Time-reversal symmetry is no longer exact; probability conservation becomes approximate within subsystems; and information loss is treated as a physical transfer into an entropy sector rather than as a mere epistemic limitation. The paper builds on these ideas to show how neutrinos—because of their weak interactions and long propagation distances—are exceptionally sensitive probes of entropic dynamics.

3. Reinterpreting Neutrino Mixing and the PMNS Matrix

In the Standard Model, neutrino oscillations arise because flavor eigenstates are superpositions of mass eigenstates. The PMNS matrix encodes this mismatch, but its structure remains unexplained. The paper proposes that entropy-driven mixing mechanisms may provide a natural explanation.

Two complementary ideas are developed. First, entropy maximization arguments suggest that large mixing angles can emerge as equilibrium configurations in the early universe or other high-entropy environments. Second, explicit coupling between neutrinos and the entropy field can induce flavor-changing effects analogous to open quantum system dynamics. In this picture, neutrino flavor transitions are not purely unitary oscillations but may involve subtle exchanges of entropy with an underlying reservoir.

These mechanisms offer new intuition for why two mixing angles are large, one is smaller, and why neutrinos differ qualitatively from quarks.

4. CPT Symmetry and Entropy-Induced Time Asymmetry

A central conceptual advance of the paper is its treatment of CPT symmetry. Conventional quantum field theory guarantees CPT invariance under broad assumptions, including unitarity and time-reversal symmetry. ToE challenges these assumptions by introducing a fundamental arrow of time through entropy flow.

Rather than abandoning CPT entirely, the paper proposes a generalized CPT* symmetry in which CPT invariance is restored only when entropy conjugation is included. This leads to the possibility that neutrinos and antineutrinos experience slightly different effective dynamics due to asymmetric coupling to entropy. Such effects could manifest as tiny differences in oscillation parameters, decoherence rates, or CP-violating phases—effects that next-generation experiments may be able to probe.

5. Entropic Noether’s Theorem and Modified Conservation Laws

The introduction of entropy as a dynamical field necessitates a generalization of Noether’s theorem. The paper formulates an Entropic Noether’s principle, according to which symmetries broken by entropy coupling lead to modified continuity equations with entropy-dependent source terms.

Applied to neutrino physics, this framework opens the door to controlled violations of lepton number and lepton flavor conservation. Such violations may appear as non-unitarity, exotic decay channels, or apparent anomalies in oscillation data. Importantly, these effects are not arbitrary but are quantitatively linked to entropy production, preserving a deeper generalized conservation structure.

6. Thermodynamic Uncertainty and the Entropic Time Limit

Another key contribution of the paper is the extension of quantum uncertainty principles to include entropy. By placing energy and entropy on equal footing, the theory introduces an entropic time limit—a fundamental minimum duration for physical processes.

When applied to neutrino oscillations, this principle suggests new bounds on coherence lengths, oscillation speeds, and decoherence mechanisms. While current experiments are unlikely to be directly sensitive to such effects, extreme environments such as supernovae, the early universe, or ultra-long-baseline propagation may reveal signatures of entropy-limited dynamics.

7. Phenomenology and Experimental Outlook

The final sections translate the theoretical framework into phenomenological consequences. The paper discusses how entropy-induced decoherence could slightly damp oscillation probabilities, how CP violation might acquire environment-dependent corrections, and how the neutrino mass hierarchy and Dirac–Majorana nature could be reinterpreted within an entropic framework.

Crucially, the work outlines potential tests using current and upcoming experiments such as T2K, NOνA, DUNE, JUNO, and Hyper-Kamiokande. While ToE effects are expected to be subtle, their cumulative impact over long baselines or high-entropy conditions may eventually distinguish them from conventional new-physics scenarios.

8. Conceptual Significance

Beyond specific predictions, the paper makes a broader conceptual claim: neutrino physics may be one of the first domains where the dynamical role of entropy becomes experimentally relevant. By linking mixing, CP violation, irreversibility, and information flow within a single framework, the Theory of Entropicity offers a unifying perspective that challenges the traditional separation between thermodynamics and fundamental particle physics.

In this sense, the work positions neutrinos not merely as particles with tiny masses, but as windows into the deep entropic structure of physical law itself.

Further Notes on Application of the Theory of Entropicity (ToE) to the Physics of Neutrinos

For decades, neutrinos have been quietly unsettling our understanding of the universe.

They pass through Earth in astronomical numbers, barely interacting, almost ghostlike. And yet, these elusive particles do something profoundly strange: they change identity as they travel. A neutrino created as one “flavor” can later be detected as another. This phenomenon — neutrino oscillation — is now well established and mathematically encoded in the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix.

But here is the uncomfortable truth: while the PMNS matrix works astonishingly well, it explains nothing about why it is the way it is.

Why are the mixing angles so large compared to those of quarks?
Why does the lepton sector seem predisposed to strong CP violation?
Why does neutrino physics feel so different from the rest of the Standard Model?

The Theory of Entropicity (ToE) begins from a radical but increasingly unavoidable suspicion: perhaps the missing ingredient is entropy — not as a statistical afterthought, but as a fundamental physical actor.

The Uneasy Status of Entropy in Fundamental Physics

Entropy is everywhere in physics, yet nowhere at its foundations.

It governs the arrow of time, limits computation, shapes black holes, and dictates thermodynamic behavior. But in particle physics and quantum field theory, entropy is usually treated as a bookkeeping tool — something we calculate after the fact, not something that acts.

This uneasy separation has always been philosophically troubling. The laws of motion are time-reversible, yet the universe is not. Quantum mechanics is unitary, yet measurement is irreversible. Field theories are symmetric, yet physical processes are directional.

The Theory of Entropicity takes these tensions seriously and proposes a bold resolution: entropy is not merely a measure of disorder — it is a dynamical field that participates in physical law.

Once this idea is accepted, neutrinos emerge as natural messengers of entropic physics.

Why Neutrinos Are the Perfect Entropic Probes

Neutrinos are unlike any other known particles. They interact weakly, travel immense distances, and retain quantum coherence far longer than most systems. If entropy subtly influences quantum evolution, neutrinos are among the few particles capable of revealing it.

In conventional treatments, neutrino oscillations are purely unitary phenomena. A neutrino’s flavor changes because mass eigenstates accumulate different phases during propagation. Entropy plays no direct role.

ToE challenges this picture by asking a deeper question: what if neutrino oscillations occur within an entropic background that is itself evolving?

In such a setting, flavor change is no longer just a geometric rotation in Hilbert space. It becomes a process influenced by entropy flow, information redistribution, and irreversible coupling to an entropic field.

The PMNS matrix, from this perspective, is not merely a mixing matrix. It is a thermodynamic fingerprint.

Entropy as a Driver of Mixing, Not Just a Spectator

One of the most striking features of neutrino physics is the size of its mixing angles. Two of them are large — almost maximal — while the quark sector shows only small mixings. The Standard Model offers no explanation for this contrast.

Within the Theory of Entropicity, this disparity becomes less mysterious.

Entropy tends to favor configurations that maximize accessible states and information flow. Large mixing angles correspond to states that are more entropically connected, more delocalized in flavor space, and less constrained by symmetry. In high-entropy environments — such as the early universe — such configurations are not accidental; they are favored.

Neutrino mixing, in this view, is not arbitrary. It is entropically natural.

CP Violation, Time’s Arrow, and the Entropic Asymmetry

Perhaps the most profound implication of introducing entropy as a fundamental field lies in its relationship to time.

Entropy is inherently directional. It distinguishes past from future. By embedding entropy directly into fundamental dynamics, ToE introduces a subtle but unavoidable time asymmetry into particle physics.

This has direct consequences for CP and CPT symmetries.

Standard quantum field theory guarantees CPT invariance under broad assumptions, including exact unitarity and time reversibility. ToE relaxes these assumptions — not by discarding them recklessly, but by extending them. It proposes that CPT symmetry must be generalized to include entropy conjugation.

In this framework, neutrinos and antineutrinos may experience slightly different entropic environments, leading to effective asymmetries that resemble CP violation. Crucially, these effects arise not from arbitrary symmetry breaking, but from the same entropic mechanisms that define the arrow of time itself.

Suddenly, CP violation in the lepton sector is no longer an isolated mystery. It becomes part of a deeper story about irreversibility.

Conservation Laws Revisited: An Entropic Noether Principle

One of the most unsettling ideas in the Theory of Entropicity is that traditional conservation laws may not be absolute within subsystems.

This does not mean energy or lepton number simply disappear. Rather, ToE proposes that conservation laws must be generalized to include entropy flow.

When entropy couples dynamically to matter, symmetries give rise not to strict conservation equations, but to balance laws with entropic source terms. This is formalized through an Entropic Noether principle.

Applied to neutrinos, this opens the door to small, controlled deviations from perfect unitarity — effects that could appear as decoherence, apparent non-conservation, or anomalous oscillation behavior.

These deviations are not arbitrary. They are tightly constrained by entropy production itself.

The Entropic Time Limit and Quantum Evolution

Another striking idea introduced in the paper is the existence of a fundamental entropic time limit.

Just as quantum mechanics limits how precisely energy and time can be simultaneously defined, ToE suggests that entropy imposes a minimum timescale on physical processes. No interaction can occur faster than the rate at which entropy can reorganize.

For neutrinos, this implies subtle bounds on coherence lengths, oscillation speeds, and flavor transition rates. While such effects are likely tiny, they may become relevant over cosmic distances or in extreme astrophysical environments.

Once again, neutrinos appear as ideal laboratories for probing the deep structure of physical law.

What Experiments Might See

The Theory of Entropicity does not reject existing neutrino experiments; it invites them to look closer.

Long-baseline experiments such as T2K, NOνA, DUNE, and JUNO already test neutrino oscillations with extraordinary precision. ToE predicts that, beyond the Standard Model parameters, there may exist faint signatures of entropic coupling: environment-dependent CP phases, tiny decoherence effects, or deviations from perfect unitarity that accumulate over long distances.

None of these effects would overthrow existing data. They would refine it.

In this sense, ToE does not compete with the Standard Model — it extends its interpretive reach.

A Broader Shift in Perspective

At its deepest level, this work is not only about neutrinos.

It is about the role of entropy in fundamental physics.

Recent developments in quantum information theory, black hole physics, and thermodynamics increasingly suggest that entropy and information are not peripheral concepts. They are structural. The Theory of Entropicity embraces this trend and pushes it further, proposing that entropy is the substrate from which geometry, quantum behavior, and symmetry itself emerge.

Neutrinos, with their quiet strangeness, may be among the first particles to reveal this hidden layer of reality.

Final Thought: From Ghost Particles to Entropic Messengers

Neutrinos were once thought to be massless. Then almost irrelevant. Now they sit at the center of some of the deepest questions in physics.

The Theory of Entropicity (ToE) suggests that their true role may be even more profound. They may be messengers — not just of physics beyond the Standard Model, but of a deeper entropic architecture underlying all physical law.

If that is the case, then the PMNS matrix is not merely a numerical artifact.

It is a window into how entropy shapes the universe at its most fundamental level.

App Deployment on the Theory of Entropicity (ToE):

App on the Theory of Entropicity (ToE): Click or Open on web browser (a GitHub Deployment - WIP): Theory of Entropicity (ToE)

https://phjob7.github.io/JOO_1PUBLIC/index.html

Sources — help

References

Obidi, John Onimisi (27th December, 2025). The Theory of Entropicity (ToE) Goes Beyond Holographic Pseudo-Entropy: From Boundary Diagnostics to a Universal Entropic Field Theory. Figshare. https://doi.org/10.6084/m9.figshare.30958670
Obidi, John Onimisi. (12th November, 2025). On the Theory of Entropicity (ToE) and Ginestra Bianconi’s Gravity from Entropy: A Rigorous Derivation of Bianconi’s Results from the Entropic Obidi Actions of the Theory of Entropicity (ToE). Cambridge University. https//doi.org/10.33774/coe-2025-g7ztq
John Onimisi Obidi. (6th November, 2025). Comparative analysis between john onimisi obidi’s theory of entropicity (toe) and waldemar marek feldt’s feldt–higgs universal bridge (f–hub) theory. International Journal of Current Science Research and Review, 8(11), pp. 5642–5657, 19th November 2025. URL: https://doi.org/10.47191/ijcsrr/V8-i11–21
Obidi, John Onimisi. 2025. On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. Cambridge University. Published October 17, 2025. https://doi.org/10.33774/coe-2025-1dsrv
Obidi, John Onimisi (17th October 2025). On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. Figshare. https://doi.org/10.6084/m9.figshare.30337396.v2
Obidi, John Onimisi. 2025. A Simple Explanation of the Unifying Mathematical Architecture of the Theory of Entropicity (ToE): Crucial Elements of ToE as a Field Theory. Cambridge University. Published October 20, 2025. https://doi.org/10.33774/coe-2025-bpvf3
Obidi, John Onimisi (15 November 2025). The Theory of Entropicity (ToE) Goes Beyond Holographic Pseudo-Entropy: From Boundary Diagnostics to a Universal Entropic Field Theory. Figshare. https://doi.org/10.6084/m9.figshare.30627200.v1
Obidi, John Onimisi. Unified Field Architecture of Theory of Entropicity (ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59276 (accessed on 19 November 2025).
Obidi, John Onimisi. (4 November, 2025). The Theory of Entropicity (ToE) Derives Einstein’s Relativistic Speed of Light © as a Function of the Entropic Field: ToE Applies Logical Entropic Concepts and Principles to Derive Einstein’s Second Postulate. Cambridge University. https://doi.org/10.33774/coe-2025-f5qw8-v2
Obidi, John Onimisi. (28 October, 2025). The Theory of Entropicity (ToE) Derives and Explains Mass Increase, Time Dilation and Length Contraction in Einstein’s Theory of Relativity (ToR): ToE Applies Logical Entropic Concepts and Principles to Verify Einstein’s Relativity. Cambridge University. https://doi.org/10.33774/coe-2025-6wrkm
HandWiki contributors, “Physics:Theory of Entropicity (ToE) Derives Einstein’s Special Relativity,” HandWiki, https://handwiki.org/wiki/index.php?title=Physics:Theory_of_Entropicity_(ToE)_Derives_Einstein%27s_Special_Relativity&oldid=3845936

Further Resources on the Theory of Entropicity (ToE):

Website: Theory of Entropicity ToE — https://theoryofentropicity.blogspot.com
LinkedIn: Theory of Entropicity ToE — https://www.linkedin.com/company/theory-of-entropicity-toe/about/?viewAsMember=true
Notion-1: Theory of Entropicity (ToE)
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Substack: Theory of Entropicity (ToE) — John Onimisi Obidi | Substack
Medium: Theory of Entropicity (ToE) — John Onimisi Obidi — Medium
SciProfiles: Theory of Entropicity (ToE) — John Onimisi Obidi | Author
Encyclopedia.pub: Theory of Entropicity (ToE) — John Onimisi Obidi | Author
HandWiki contributors, “Biography: John Onimisi Obidi,” HandWiki, https://handwiki.org/wiki/index.php?title=Biography:John_Onimisi_Obidi&oldid=2743427 (accessed October 31, 2025).
HandWiki Contributions: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki
HandWiki Home: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki
HandWiki Homepage-User Page: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki
Academia: Theory of Entropicity (ToE) — John Onimisi Obidi | Academia
ResearchGate: Theory of Entropicity (ToE) — John Onimisi Obidi | ResearchGate
Figshare: Theory of Entropicity (ToE) — John Onimisi Obidi | Figshare
Authoria: Theory of Entropicity (ToE) — John Onimisi Obidi | Authorea
Social Science Research Network (SSRN): Theory of Entropicity (ToE) — John Onimisi Obidi | SSRN
Wikidata contributors, Biography: John Onimisi Obidi “Q136673971,” Wikidata, https://www.wikidata.org/w/index.php?title=Q136673971&oldid=2423782576 (accessed November 13, 2025).
Google Scholar: ‪John Onimisi Obidi — ‪Google Scholar
IJCSRR: International Journal of Current Science Research and Review - Theory of Entropicity (ToE) - John Onimisi Obidi | IJCSRR
Cambridge University Open Engage (CoE): Collected Papers on the Theory of Entropicity (ToE)

Theory of Entropicity (ToE) by John Onimisi Obidi

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Monday, 29 December 2025