Entropic Dynamics on Curved Spaces

TL;DR

This paper extends entropic dynamics to curved spaces, deriving a modified Schrödinger equation with the Laplace-Beltrami operator to account for curvature effects on particle fluctuations.

Contribution

It introduces a novel formulation of entropic dynamics on curved spaces, incorporating curvature effects into quantum evolution equations.

Findings

Derived a modified Schrödinger equation with Laplace-Beltrami operator

Showed fluctuations are affected by space curvature

Extended entropic dynamics framework to non-flat geometries

Abstract

Entropic dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. Entropic dynamics on flat spaces has been extensively studied. The objective of this paper is to extend the entropic dynamics of $N$ particles to curved spaces. The important new feature is that the displacement of a particle does not transform like a vector because fluctuations can be large enough to feel the effects of curvature. The final result is a modified Schr\"odinger equation in which the usual Laplacian is replaced by the Laplace-Beltrami operator.