  We introduce a new formalism for computing expectations of functionals of
arbitrary random vectors, by using generalised integration by parts formulae.
In doing so we extend recent representation formulae for the score function
introduced in Nourdin, Peccati and Swan (JFA, to appear) and also provide a new
proof of a central identity first discovered in Guo, Shamai, and Verd{\'u}
(IEEE Trans. Information Theory, 2005). We derive a representation for the
standardized Fisher information of sums of i.i.d. random vectors which use our
identities to provide rates of convergence in information theoretic central
limit theorems (both in Fisher information distance and in relative entropy).
