Non-equilibrium statistical field theory for classical particles:
  Initially correlated grand canonical ensembles
  It was recently shown by Bartelmann et al. how correlated initial conditions
can be introduced into the statistical field theory for classical particles
pioneered by Das and Mazenko. In this paper we extend this development from the
canonical to the grand canonical ensemble for a system satisfying statistical
homogeneity and isotropy. We do this by translating the probability
distribution for the initial phase space coordinates of the particles into an
easy diagrammatic representation and then using a variant of the Mayer cluster
expansion to sum over particle numbers. The grand canonical generating
functional is then used in a structured approach to the derivation of the
non-interacting cumulants of the two core collective fields, the density $\rho$
and the response field $B$. As a side-product we find several theorems
pertaining to these cumulants which will be useful when investigating the
interacting regime of the theory in future work.
