Intrinsic probability distributions for physical systems

TL;DR

This paper introduces a method to derive intrinsic probability distributions for physical systems by optimizing the Fisher information metric under given constraints, resulting in differential equations that define these distributions.

Contribution

It proposes a novel approach to determine intrinsic probability distributions in physical systems using Fisher information optimization, providing a new theoretical framework.

Findings

Derived differential equations for probability distributions.

Established a link between Fisher information and physical system constraints.

Provided a new perspective on intrinsic distributions in physics.

Abstract

For a given metric $g_{\mu\nu}$, which is identified as Fisher information metric, we generate new constraints for the probability distributions for physical systems. We postulate the existence of intrinsic probability distributions for physical systems, and calculate the probability distribution by optimizing the Fisher information metric under specified constraints. Accordingly, we get differential equations for the probability distributions.