On two properties of the Fisher information

Nicolas Rougerie

doi:10.3934/krm.2020049

Article Contents

2021, Volume 14, Issue 1: 77-88. Doi: 10.3934/krm.2020049

This issue Previous Article Opinion formation systems via deterministic particles approximation Next Article Superposition principle and schemes for measure differential equations

On two properties of the Fisher information

Nicolas Rougerie

Université Grenoble-Alpes & CNRS, LPMMC (UMR 5493), B.P. 166, F-38042 Grenoble, France

Received: January 2020

Revised: August 2020

Early access: November 2020

Published: February 2021

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Abstract

Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that such informations can be interpreted as quantum kinetic energies.

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Mathematics Subject Classification: Primary: 82Bxx, 35Qxx; Secondary: 49Sxx.

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