Fisher information, Wehrl entropy, and Landau Diamagnetism

TL;DR

This paper explores the thermodynamics of Landau diamagnetism using information theory, revealing a new Fisher-uncertainty relation linking phase space localization and energy fluctuations.

Contribution

It introduces a novel Fisher-uncertainty relation derived from the Cramer-Rao inequality in the context of Landau diamagnetism, connecting information measures with physical properties.

Findings

Established a link between Wehrl entropy and Landau diamagnetism.

Discovered a new Fisher-uncertainty relation involving phase space and energy.

Mapped the problem to a thermal harmonic oscillator model.

Abstract

Using information theoretic quantities like the Wehrl entropy and Fisher's information measure we study the thermodynamics of the problem leading to Landau's diamagnetism, namely, a free spinless electron in a uniform magnetic field. It is shown that such a problem can be "translated" into that of the thermal harmonic oscillator. We discover a new Fisher-uncertainty relation, derived via the Cramer-Rao inequality, that involves phase space localization and energy fluctuations.