Towards Abel Prize: The Generalized Brownian Motion Manifold's Fisher Information Matrix With Info-Geometric Applications to Energy Works

Abstract

The current paper provides a giant step ahead towards a revolutionary info-geometric unification with Generalized Brownian motion manifold (GBMM). More potentially, a new info-geometric limitation for the rescaling parameter of the GBMM is revealed, which was never known before in physics. Clearly, this emphasizes the potential role of Information geometry (IG) to re- study the dynamics of GBMM rather than other known classical approaches. In principle, the Shared Abel Prize (Noble Prize of Mathematics) 2020 between Furstenberg and Margulis surprised the academic community by their brilliant application of probabilistic techniques and random walks to resolve challenging issues in a variety of mathematical disciplines. This indicates the ultimate significance of the undertaken novel approach in this paper since we IG is employed to start a first ever investigation of Generalized Brownian Motion (GBM) which is the ultimate generalization to random walks. This provides more stunning mathematical insight to a unified contemporary analysis of GBM. This current work both generalizes and supersedes Furstenberg and Margulis. More interestingly, influential applications of Information geometry (IG) and Brownian Motion (BM) to energy works are overviewed. Fundamentally, the current work opens new frontiers to the info-geometry theory of Generalized Brownian Motion (IGBM) as well as the provision of new insights about the potential IG applications to all researchers in the field of energy.