  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.
