  We use complex contour integral techniques to study the entropy H and
subentropy Q as functions of the elementary symmetric polynomials, revealing a
series of striking properties. In particular for these variables, derivatives
of -Q are equal to derivatives of H of one higher order and the first
derivatives of H and Q are seen to be completely monotone functions. It then
follows that exp (-H) and exp(-Q) are Laplace transforms of infinitely
divisible probability distributions.
