Fisher Information and Kinetic-energy Functionals: A Dequantization Approach

TL;DR

This paper introduces a dequantization approach that decomposes quantum kinetic energy into classical and quantum parts, linking Fisher information with quantum fluctuations and enhancing understanding of kinetic-energy functionals.

Contribution

It presents a novel dequantization method that connects Fisher information with quantum kinetic energy, providing new insights into kinetic-energy functionals in quantum systems.

Findings

Decomposition of quantum kinetic energy into classical and quantum components.

Identification of the quantum component as Fisher information.

Application to stationary and nonstationary quantum states.

Abstract

We strengthen the connection between Information Theory and quantum-mechanical systems using a recently developed dequantization procedure whereby quantum fluctuations latent in the quantum momentum are suppressed. The dequantization procedure results in a decomposition of the quantum kinetic energy as the sum of a classical term and a purely quantum term. The purely quantum term, which results from the quantum fluctuations, is essentially identical to the Fisher information. The classical term is complementary to the Fisher information and, in this sense, it plays a role analogous to that of the Shannon entropy. We demonstrate the kinetic energy decomposition for both stationary and nonstationary states and employ it to shed light on the nature of kinetic-energy functionals.