Geometry from Information: Uniqueness of Relative Entropy as the Gravitational Potential and Canonical Realisation of the Informational Index Principle.
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| Natura: | Recurso digital |
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2026
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| _version_ | 1866901311377637376 |
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| author | Gogishvili, David |
| author_facet | Gogishvili, David |
| contents | <blockquote> <p dir="ltr">"This work establishes a unique axiomatic derivation of Einstein's field equations and the Lovelock gravity family from the principles of quantum information theory. By proving the uniqueness of relative entropy as a gravitational potential, we derive the Bogoliubov-Kubo-Mori (BKM) metric on the space of metrics. The central result provides the first canonical realization of the Informational Index Principle: identifying the Breuer-Fredholm index of an affine Dirac operator in the Type II$_{\infty}$ crossed-product factor as the Euler characteristic \chi(M)=2. This resolves a fundamental open problem in the operator-algebraic foundation of de Sitter space by uniquely determining the abstract spectral triple through modular data."</p> </blockquote> <p dir="ltr"> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18859097 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Geometry from Information: Uniqueness of Relative Entropy as the Gravitational Potential and Canonical Realisation of the Informational Index Principle. Gogishvili, David Quantum Information Theory. Relative Entropy. Lovelock Gravity. Type III Factors. Breuer-Fredholm Index. de Sitter Space. Modular Theory (Tomita-Takesaki). <blockquote> <p dir="ltr">"This work establishes a unique axiomatic derivation of Einstein's field equations and the Lovelock gravity family from the principles of quantum information theory. By proving the uniqueness of relative entropy as a gravitational potential, we derive the Bogoliubov-Kubo-Mori (BKM) metric on the space of metrics. The central result provides the first canonical realization of the Informational Index Principle: identifying the Breuer-Fredholm index of an affine Dirac operator in the Type II$_{\infty}$ crossed-product factor as the Euler characteristic \chi(M)=2. This resolves a fundamental open problem in the operator-algebraic foundation of de Sitter space by uniquely determining the abstract spectral triple through modular data."</p> </blockquote> <p dir="ltr"> </p> |
| title | Geometry from Information: Uniqueness of Relative Entropy as the Gravitational Potential and Canonical Realisation of the Informational Index Principle. |
| topic | Quantum Information Theory. Relative Entropy. Lovelock Gravity. Type III Factors. Breuer-Fredholm Index. de Sitter Space. Modular Theory (Tomita-Takesaki). |
| url | https://doi.org/10.5281/zenodo.18859097 |