## Nested sums (entropies): can this expression be simplified?

Is it possible to combine the sums this expression, and thereby reduce the expression? I don't think so but I might be missing something.

$\sum_{W} p(w) log(\frac{1}{p(w)}) + \sum_{X} \sum_{W} p(x,w) log(p(x,w)) + \sum_{Y} \sum_{W} p(y,w) log(p(y,w)) + \sum_{X} \sum_{Y} \sum_{W} p(x,y,w) log(\frac{1}{p(x,y,w)})$