Escort--Husimi distributions, Fisher information and nonextensivity

TL;DR

This paper explores generalized information measures using Husimi distributions, linking them to Wehrl entropy and thermal uncertainty, and introduces a new interpretation of the nonextensivity index q with a physical lower bound.

Contribution

It provides a novel interpretation of the nonextensivity index q and establishes a state equation transforming the escort-Cramer--Rao bound into a thermal uncertainty relation.

Findings

A physical lower bound for q is derived.

A new interpretation of the nonextensivity index q is proposed.

The escort-Cramer--Rao bound is transformed into a thermal uncertainty relation.

Abstract

We evaluate generalized information measures constructed with Husimi distributions and connect them with the Wehrl entropy, on the one hand, and with thermal uncertainty relations, on the other one. The concept of escort distribution plays a central role in such a study. A new interpretation concerning the meaning of the nonextensivity index $q$ is thereby provided. A physical lower bound for $q$ is also established, together with a ``state equation" for $q$ that transforms the escort-Cramer--Rao bound into a thermal uncertainty relation.