# Relative Entropy and Tsallis Entropy of two Accretive Operators

## TL;DR

This paper extends the concepts of relative entropy and Tsallis entropy to accretive operators, introducing a weighted geometric mean and exploring related properties, thereby broadening the scope beyond positive invertible operators.

## Contribution

It introduces new definitions of relative and Tsallis entropy for accretive operators and studies their properties, extending existing concepts from positive invertible operators.

## Key findings

- Defined weighted geometric mean for accretive operators
- Extended relative entropy and Tsallis entropy to accretive operators
- Established properties of these entropies in the new context

## Abstract

Let $A$ and $B$ be two accretive operators. We first introduce the weighted geometric mean of $A$ and $B$ together with some related properties. Afterwards, we define the relative entropy as well as the Tsallis entropy of $A$ and $B$. The present definitions and their related results extend those already introduced in the literature for positive invertible operators.