  For thermal equilibrium systems it is shown, how the Kubo-Martin-Schwinger
boundary condition may be used to factorize the generating functional of Green
functions at least on the level of the full two-point function. Genuine
non-equilibrium system exhibit correlations that one may also incorporate in
the path integral. One one hand this provides a natural tool for a perturbative
expansion including these correlations. On the other hand it allows to prove
that in general non-equilibrium systems the generating functional does not
factorize.
