Mechanics of geodesics in Information geometry and Black Hole Thermodynamics

In this article we attempt to formulate Riemannian and Randers-Finsler metrics in information geometry and study their mechanical properties. Starting from the gradient flow equations, we show how to formulate Riemannian metrics, and demonstrate their duality under canonical transformation. Then we show how to formulate a Randers-Finsler metric from deformed gradient equations. The theories described are applied to the Gaussian model and tested to verify consistency and also to Reissner-Nordstrom and Kerr black holes.