Relativistic Hamiltonian as an emergent structure from information geometry
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913096301281280 |
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| author | Yoo-Kong, Sikarin |
| author_facet | Yoo-Kong, Sikarin |
| contents | We show that the relativistic energy-momentum relation can emerge as an effective ensemble-averaged structure from a multiplicative Hamiltonian when fluctuations of an auxiliary parameter are treated using maximum entropy inference. The resulting probability distribution is uniquely fixed by scale-invariant constraints, which are shown to arise naturally from the Fisher-Rao geometry of the associated statistical manifold. Within this information-geometric framework, the relativistic dispersion relation appears without initially imposing Lorentz symmetry, but as a consequence of statistical averaging and geometric invariance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Relativistic Hamiltonian as an emergent structure from information geometry Yoo-Kong, Sikarin Mathematical Physics Information Theory Classical Physics We show that the relativistic energy-momentum relation can emerge as an effective ensemble-averaged structure from a multiplicative Hamiltonian when fluctuations of an auxiliary parameter are treated using maximum entropy inference. The resulting probability distribution is uniquely fixed by scale-invariant constraints, which are shown to arise naturally from the Fisher-Rao geometry of the associated statistical manifold. Within this information-geometric framework, the relativistic dispersion relation appears without initially imposing Lorentz symmetry, but as a consequence of statistical averaging and geometric invariance. |
| title | Relativistic Hamiltonian as an emergent structure from information geometry |
| topic | Mathematical Physics Information Theory Classical Physics |
| url | https://arxiv.org/abs/2601.12764 |