A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-11, author = {Fumio Hiai and D\'enes Petz}, title = {A new approach to mutual information}, journal = {Banach Center Publications}, volume = {75}, year = {2007}, pages = {151-164}, zbl = {05235290}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-11} }
Fumio Hiai; Dénes Petz. A new approach to mutual information. Banach Center Publications, Tome 75 (2007) pp. 151-164. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-11/