| _version_ | 1866901901822394368 |
|---|---|
| author | Alemsefa, Addisu |
| author_facet | Alemsefa, Addisu |
| contents | <p>This is Version 5 of the work. It introduces a variational principle for the informational metric, derives equations of motion, and presents a modified quantum evolution, It includes a dynamical derivation of the informational metric and introduces a testable prediction for entropy-dependent entanglement growth.This work proposes a theoretical framework in which entropy is treated as a geometric degree of freedom in an extended quantum state space. By introducing a resolution parameter defined as the inverse of von Neumann entropy, an informational metric is constructed on the space of density matrices.</p> <p>Within this framework, a causal structure emerges from a null condition on the metric, defining a light-cone-like boundary for the propagation of quantum correlations. Entanglement propagation is derived and shown to depend on entropy evolution, leading to a dynamical causal structure. In the near-equilibrium limit, the model reproduces a Lieb–Robinson-type bound with finite correlation speed.</p> <p>Connections to holography are established by interpreting entropy as a radial coordinate controlling scale, and an analogue of the Ryu–Takayanagi relation is derived, where entropy corresponds to the length of minimal curves in the informational geometry.</p> <p>Black hole horizons are interpreted as maximal entropy surfaces corresponding to a collapse of distinguishability in quantum state space. The framework suggests that spacetime geometry, causality, and gravitational behavior may emerge from entropy-weighted quantum information structure.</p> <p>This work is an independent theoretical exploration aimed at providing a unified perspective linking quantum information, geometry, and gravity.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19288515 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | entropy_geometric_dimension_informational_metric.pdf Alemsefa, Addisu <p>This is Version 5 of the work. It introduces a variational principle for the informational metric, derives equations of motion, and presents a modified quantum evolution, It includes a dynamical derivation of the informational metric and introduces a testable prediction for entropy-dependent entanglement growth.This work proposes a theoretical framework in which entropy is treated as a geometric degree of freedom in an extended quantum state space. By introducing a resolution parameter defined as the inverse of von Neumann entropy, an informational metric is constructed on the space of density matrices.</p> <p>Within this framework, a causal structure emerges from a null condition on the metric, defining a light-cone-like boundary for the propagation of quantum correlations. Entanglement propagation is derived and shown to depend on entropy evolution, leading to a dynamical causal structure. In the near-equilibrium limit, the model reproduces a Lieb–Robinson-type bound with finite correlation speed.</p> <p>Connections to holography are established by interpreting entropy as a radial coordinate controlling scale, and an analogue of the Ryu–Takayanagi relation is derived, where entropy corresponds to the length of minimal curves in the informational geometry.</p> <p>Black hole horizons are interpreted as maximal entropy surfaces corresponding to a collapse of distinguishability in quantum state space. The framework suggests that spacetime geometry, causality, and gravitational behavior may emerge from entropy-weighted quantum information structure.</p> <p>This work is an independent theoretical exploration aimed at providing a unified perspective linking quantum information, geometry, and gravity.</p> |
| title | entropy_geometric_dimension_informational_metric.pdf |
| url | https://doi.org/10.5281/zenodo.19288515 |