Reconciling Thermodynamics and Quantum Mechanics with the Harmonic Divisor Fan (HDF) Lattice.
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2025
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| _version_ | 1866902217871589376 |
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| author | Okolo, Hanyelichukwu Paul |
| author_facet | Okolo, Hanyelichukwu Paul |
| contents | <div> <div> <div> <p>This paper derives the foundational laws of thermodynamics and quantum mechanics as emergent phenomena from the Harmonic Divisor Fan (HDF) lattice, a discrete arithmetic structure rooted in posi- tive integers and prime multiplications. We provide a thorough definition of the HDF lattice and its parameters, including the state field Ψ, vorticity S(t), and master equation. Through a detailed proof strategy, we define lattice entropy and prove the Second Law from structured dissipation, establishing a deterministic origin for irreversibility. For quantum mechanics, we derive the Schr ̈odinger equation in the low-energy limit, with explicit construction of the Hamiltonian Hˆ and emergence of the imaginary unit i from vorticity-phase coupling, ensuring unitarity. This unifies number theory with physics, linking the Riemann Hypothesis resolution via S(t) to entropy growth and quantum uncertainty.</p> </div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15864820 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Reconciling Thermodynamics and Quantum Mechanics with the Harmonic Divisor Fan (HDF) Lattice. Okolo, Hanyelichukwu Paul Thermodynamics Thermodynamics Quantum Mechanics Number Theory <div> <div> <div> <p>This paper derives the foundational laws of thermodynamics and quantum mechanics as emergent phenomena from the Harmonic Divisor Fan (HDF) lattice, a discrete arithmetic structure rooted in posi- tive integers and prime multiplications. We provide a thorough definition of the HDF lattice and its parameters, including the state field Ψ, vorticity S(t), and master equation. Through a detailed proof strategy, we define lattice entropy and prove the Second Law from structured dissipation, establishing a deterministic origin for irreversibility. For quantum mechanics, we derive the Schr ̈odinger equation in the low-energy limit, with explicit construction of the Hamiltonian Hˆ and emergence of the imaginary unit i from vorticity-phase coupling, ensuring unitarity. This unifies number theory with physics, linking the Riemann Hypothesis resolution via S(t) to entropy growth and quantum uncertainty.</p> </div> </div> </div> |
| title | Reconciling Thermodynamics and Quantum Mechanics with the Harmonic Divisor Fan (HDF) Lattice. |
| topic | Thermodynamics Thermodynamics Quantum Mechanics Number Theory |
| url | https://doi.org/10.5281/zenodo.15864820 |