Mechanics of geodesics in Information geometry and Black Hole Thermodynamics

Abstract

In this article we shall discuss the theory of geodesics in information geometry, and an application in astrophysics. We will study how gradient flows in information geometry describe geodesics, explore the related mechanics by introducing a constraint, and apply our theory to Gaussian model and black hole thermodynamics. Thus, we demonstrate how deformation of gradient flows leads to more general Randers-Finsler metrics, describe Hamiltonian mechanics that derive from a constraint, and prove duality via canonical transformation. We also verified our theories for a deformation of the Gaussian model, and described dynamical evolution of flat metrics for Kerr and Reissner-Nordström black holes.

24 pages. Corrections made. New section and 2 references added. Please comment

References in corpus (4)

• Flat Information Geometries in Black Hole Thermodynamics
• Jacobi-Maupertuis Randers-Finsler metric for curved spaces and the gravitational magnetoelectric effect
• Comparing metrics for mixed quantum states: Sjoqvist and Bures
• An eikonal equation approach to thermodynamics and the gradient flows in information geometry

Cited by in corpus (1)

• A Hamiltonian approach to the gradient-flow equations in information geometry