  We present a formula for the relative entropy S(rho||sigma) of two n mode
gaussian states rho, sigma in the boson Fock space. It is shown that the
relative entropy has a classical and a quantum part: The classical part
consists of a weighted linear combination of relative Shannon entropies of $n$
pairs of Bernouli trials arising from the thermal state composition of the
gaussian states rho and sigma. The quantum part has a sum of n terms, that are
functions of the annihilation means and the covariance matrices of 1-mode
marginals of the gaussian state rho', which is equivalent to rho under
disentangling unitary gaussian symmetry operation of the state sigma.
