Information geometry and the inverse problem for a noncommutative system

Abstract

We investigate a coupled harmonic oscillator system within a noncommutative space using the framework of information geometry. Specifically, we examine the case where position variables fail to commute. After applying a Bopp shift and performing a series of transformations to the Hamiltonian, we derive the thermodynamic potential and compute the Fisher information metric. Our results demonstrate that the space characterized by this system is half of three-dimensional flat Euclidean space with z ≤ 0. Furthermore, the commuting limit is the z = 0 plane.