A great pedagogical article on thermodynamic vs logical reversibility, for those interested: https://arxiv.org/abs/1311.1886 (Sagawa 2014).
If you don't mind my asking, how much does the role of mutual information in linking logical and thermodynamic reversibility depend on considering quantum systems? I.e. does your footnote 37, which discusses independent systems vs "subsystems of correlated systems" hold for classical systems as well?