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)

We explore how the recently proposed Theory of Entropicity (ToE)– a framework in which entropy is treated as a fundamental dynamical field– yields new insights into neutrino physics, par ticularly the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix and associated phenomena. We show that entropy-driven dynamics can induce neutrino flavor mixing, offering a fresh mech anism for generating the observed PMNS matrix structure. The entropic framework necessitates a reinterpretation of CPT symmetry: by explicitly breaking time-reversal invariance via entropy flow, a modified CPT invariant can be restored, with distinct entropy dynamics for matter and antimatter. An Entropic Noether’s theorem is formulated, linking modified conservation laws to entropy-related symmetry transformations. Furthermore, we introduce a thermodynamic uncertainty principle that treats energy and entropy on equal footing, leading to an entropic time limit a fundamental minimum duration for quantum processes. Within this ToE paradigm, we re-examine neutrino oscillations, the mass hierarchy puzzle, CP violation in the lepton sector, the Majorana vs. Dirac nature of neutrinos, and the potential for lepton flavor violation. We discuss how entropy as a field modifies oscillation probabilities, alters effective mass-squared differences, and generates environment-dependent CP-violating phases. Implications for current and upcoming experiments (T2K, NOνA, DUNE, JUNO) are examined, including possible observable deviations from Standard Model expectations due to entropic effects. This work is self-contained and emphasizes clarity and rigor, with all results derived in detail and contextualized with respect to established neutrino physics and recent experimental data.