If one is given a joint probability distribution over a finite set of discrete random variables then I guess there a notion of $\alpha-$Renyi entropy defined for it as $S_\alpha (X_1,..,X_n) = \frac{1}{1-\alpha} \log ( \sum_{a_1,..,a_n} p_{X_1,..,X_n}^\alpha (X_1 = a_1,..,X_n = a_n ) )$

Can the sum in the above is read as taking the trace of the $\alpha$ power of some density matrix?

Lets say the joint probability distribution is given as a probabilistic graphical model. Now given such a graph one can split it into sub-graphs and look at the joint distributions of each of these subgraphs. So one presumably has the $S_\alpha$ defined for each of these subgraphs. Do we have any relation between $S_\alpha (graph)$ and $\sum_{subgraphs} S_\alpha (subgraphs)$? (consider that the decomposition could be into disjoint parts or not)