A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided to the mutual information of both continuous and discrete random variables.
@article{arxiv.0704.0588,
title = {A new approach to mutual information},
author = {F. Hiai and D. Petz},
journal= {arXiv preprint arXiv:0704.0588},
year = {2007}
}