2026-04-17T11:35:25Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/2225882025-12-04T22:41:04Zcom_2072_1057col_2072_478825col_2072_478917

00925njm 22002777a 4500 dc Bernal-Casas, D. author Oller i Sala, Josep Maria author 2025-07-25T10:09:13Z 2025-07-25T10:09:13Z 2024-04-28 2025-07-25T10:09:13Z With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate normal probability distributions ( , 0), as before, but with a constant 0 not necessarily equal to 1. Then, we also relaxed the independence condition when modeling m sources of information. Now, we model m sources with a multivariate normal probability distribution ( , 0) with a constant variance–covariance matrix 0 not necessarily diagonal, i.e., with covariance values different to 0, which leads to the concept of modes rather than sources. Invoking Schrödinger’s equation, we can still break the information into m quantum harmonic oscillators, one for each mode, and with energy levels independent of the values of 0, altogether leading to the concept of “intrinsic”. Similarly, as in our previous work with the estimator’s variance, we found that the expectation of the quadratic Mahalanobis distance to the sample mean equals the energy levels of the quantum harmonic oscillator, being the minimum quadratic Mahalanobis distance at the minimum energy level of the oscillator and reaching the “intrinsic” Cramér–Rao lower bound at the lowest energy level. Also, we demonstrate that the global probability density function of the collective mode of a set of m quantum harmonic oscillators at the lowest energy level still equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. While these new assumptions certainly add complexity to the mathematical framework, the results proven are invariant under transformations, leading to the concept of “intrinsic” information-theoretic models, which are essential for developing physics. Equació de Schrödinger Estadística bayesiana Varietats de Riemann Schrödinger equation Bayesian statistical decision Riemannian manifolds Intrinsic Information-Theoretic Models