Fisher Information Perspective of Pauli's Electron

TL;DR

This paper explores the Pauli electron system as a vortical fluid, linking its internal energy to Fisher Information, and extends previous work by including electromagnetic interactions through a vector potential.

Contribution

It introduces a comprehensive analysis of the Pauli electron with electromagnetic fields, connecting Fisher Information to the system's internal energy in a novel way.

Findings

System modeled as a vortical fluid with electromagnetic interactions

Internal energy partially interpreted via Fisher Information

Extended previous models to include vector potential effects

Abstract

A non relativistic electron with a spin is described by Pauli's equation. It has been shown that this system can be interpreted as a vortical fluid which has both similarities and differences with classical ideal flows. Moreover, it was demonstrated that the internal energy of the spin fluid can partially be interpreted in terms of Fisher Information. While previous work on the subject has mainly ignored electromagnetic fields which are represented by a vector potential here we remove this limitation and study the system under general electromagnetic interaction.