🔷 Hawking Radiation in Obidi's Theory of Entropicity (ToE): Entropy‑Driven Probability Flow and the Transfer of Quantum Amplitude into the Entropic Sector—A Mechanism Built Directly into ToE

🌌 Hawking Radiation in ToE

In ToE, Hawking radiation is an entropic leakage phenomenon. It arises because black holes are not geometric objects swallowing information; they are regions of extreme entropic curvature where quantum amplitudes irreversibly flow into the entropy sector.

This mechanism is driven by the entropic operator C[S], which modifies quantum evolution and drives probability transfer into the entropy‑bound sector.

🔹 1. Entropy as a Dynamical Field (Not a Statistic) ToE elevates entropy to a real physical field—the entropic field — defined over the entropic manifold.

🧠 This field governs:

• quantum behavior
• spacetime geometry
• gravitational phenomena
• information flow

Because entropy is ontologically primary, black hole physics must be reinterpreted in terms of entropic dynamics, not geometric horizons.

🔹 2. The Entropic Operator C[S] and Probability Flow Obidi introduces an entropy‑dependent operator:

U_{{eff}}(t) = e^{-iHt}.e^{-C[S]t}

⚡ This operator:

• breaks time reversal
• drives irreversible probability flow
• creates two sectors

📌 Observable sector: (P_o(t)) 📌 Entropy‑bound sector: (P_e(t))

Obidi’s Entropic Probability Law:

Po(t) + Pe(t) = 1

This explains wavefunction collapse, classical irreversibility, and — critically — Hawking radiation, which is the re‑emergence of amplitude from the entropy sector back into the observable sector.

This is fundamentally different from the standard vacuum‑fluctuation explanation.

🔹 3. Black Holes as Entropic Curvature Wells In ToE, black holes are not geometric singularities. They are regions of maximal entropic curvature in the entropic manifold.

🌑 This means:

• A black hole’s “surface” is an entropic boundary, not a geometric horizon.
• Information entering a black hole flows into the entropy sector.
• Hawking radiation is the entropic re‑emission of information, not pair creation.

🔹 4. ToE’s Resolution of the Information Paradox ToE provides a unified explanation of the black hole information paradox:

🔸 Information is never destroyed. 🔸 It is transferred into the entropy sector via C[S]. 🔸 Hawking radiation is the mechanism by which information returns.

Thus, ToE resolves the paradox without holography, firewalls, or string theory.

🔷 Closing Remark In Obidi’s ToE:

• Hawking radiation is not caused by vacuum fluctuations.
• It emerges from entropic probability flow driven by C[S].
• Black holes are entropic curvature wells, not geometric singularities.
• Information is preserved through entropic sector dynamics.
• Radiation is a manifestation of entropy’s ontological primacy.

This makes Hawking radiation a natural and inevitable consequence of ToE’s entropic ontology, fully aligned with Informational Entropic Field.