Version 1
: Received: 24 January 2024 / Approved: 25 January 2024 / Online: 25 January 2024 (14:10:23 CET)
How to cite:
A Mageed, D. I. A Theory of Everything: When Information Geometry Meets the Generalized Brownian Motion and the Einsteinian Relativity. Preprints2024, 2024011827. https://doi.org/10.20944/preprints202401.1827.v1
A Mageed, D. I. A Theory of Everything: When Information Geometry Meets the Generalized Brownian Motion and the Einsteinian Relativity. Preprints 2024, 2024011827. https://doi.org/10.20944/preprints202401.1827.v1
A Mageed, D. I. A Theory of Everything: When Information Geometry Meets the Generalized Brownian Motion and the Einsteinian Relativity. Preprints2024, 2024011827. https://doi.org/10.20944/preprints202401.1827.v1
APA Style
A Mageed, D. I. (2024). A Theory of Everything: When Information Geometry Meets the Generalized Brownian Motion and the Einsteinian Relativity. Preprints. https://doi.org/10.20944/preprints202401.1827.v1
Chicago/Turabian Style
A Mageed, D. I. 2024 "A Theory of Everything: When Information Geometry Meets the Generalized Brownian Motion and the Einsteinian Relativity" Preprints. https://doi.org/10.20944/preprints202401.1827.v1
Abstract
Information geometry (IG) is a fascinating combination of differential geometry and statistics where a Riemannian manifold's structure is applied to a statistical model. It may find numerous fascinating uses in the domains of theoretical neurology, machine learning, complexity, and (quantum) information theory, among others. (IG) aims to provide a differential-geometric perspective on statistical geodesic models' structure. In this case, IG, KD, and J-divergence (JD) are used to define the manifold of the Generalised Brownian Motion (GBM). Consequently, the geodesic equations (GEs) are devised, and GB information matrix exponential (IME) is presented. Moreover, for first time ever, the necessary and sufficient mathematical requirement that characterizes the developability of Generalized Brownian Motion(GBM) manifold is devised. Also, a novel sufficient and necessary conditions which characterizes the regions where the surface describing GBM is minimal is determined. Also, it is shown that GBM has a non-zero 0-Gaussian and Ricci curvatures. Consequently, this advances the establishment of a unified GBM- Relativistic Info-Geometric based analysis.
Keywords
Generalized Brownian Motion (GBM), probability density function (PDF),matrix exponential of A (geodesic equations (GEs).
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
