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. Moreover, we will obtain a large deviation upper bound for a certain family of random matrices, which fits the orbital free entropy. The resulting rate function gives a new approach to `free mutual information'.

中文翻译：

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矩阵解放过程二：与轨道自由熵的关系

我们从矩阵解放过程的角度研究轨道自由熵的概念。我们将证明围绕轨道自由熵定义的许多基本问题都归结为矩阵解放过程的全大偏差原理问题。此外，我们将获得某个随机矩阵族的大偏差上限，它符合轨道自由熵。由此产生的速率函数为“自由互信息”提供了一种新方法。