Conditional Entropy on Graphs

I am studying diffusion dynamics on graphs through the lense of information theory. The discrete version of the heat kernel can be seen as a continous-time Markov Chain, and by choosing an appropriate measure of information, one can establish a mathematical formalism that replicates phenomena like the first and second laws of thermodynamics in a complex system modeles as a graph. In particular, I am focused on studying the evolution of the conditional entropy of such diffusion dynamics. Most of the results on this topic can be read in this article.