From quasi-entropy

TL;DR

This paper provides an overview of quasi-entropy in finite-dimensional spaces, highlighting its connections to matrix monotone functions, relative entropy, and divergence measures, and introduces a novel extension of the monotone metric to two variables.

Contribution

It introduces a new concept of extending the monotone metric to two variables within the framework of quasi-entropy.

Findings

Quasi-entropy encompasses relative entropy and f-divergence as special cases.

Matrix monotone functions are central to the theory.

A new extension of the monotone metric to two variables is proposed.

Abstract

The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Matrix monotone functions and relative modular operators are used. The origin is the relative entropy and the f-divergence, monotone metrics, covariance and the chi-square-divergence are the most important particular cases. The extension of the monotone metric to two variables is a new concept.