# Matrix liberation process II: Relation to orbital free entropy

## TL;DR

This paper explores the connection between orbital free entropy and matrix liberation processes, establishing large deviation principles and introducing a new approach to free mutual information.

## Contribution

It demonstrates that fundamental questions about orbital free entropy can be addressed through large deviation principles for matrix liberation processes, offering a novel perspective.

## Key findings

- Established a large deviation upper bound for certain random matrices
- Linked orbital free entropy to large deviation principles
- Proposed a new approach to free mutual information

## Abstract

We investigate the concept of orbital free entropy from the viewpoint of matrix liberation process. We will show that many basic questions around the definition of orbital free entropy are reduced to the question of full large deviation principle for the matrix liberation process. We will also obtain a large deviation upper bound for a certain family of random matrices that is an essential ingredient to define the orbital free entropy. The resulting rate function is made up into a new approach to free mutual information.