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

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On two properties of the Fisher information

Nicolas Rougerie

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

Received: December 31, 2019

Revised: July 31, 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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