  We present a derivation of the Feynman-Vernon approach to open quantum
systems in the language of super-operators. We show that this gives a new and
more direct derivation of the generating function of energy changes in a bath,
or baths. This generating function is given by a Feynman-Vernon-like influence
functional, with only time shifts in some of the kernels. We further show that
the approach can be extended to anharmonic baths by an expansion in cumulants.
Every non-zero cumulant of certain environment correlation functions thus gives
a kernel in a higher-order term in the Feynman-Vernon action.
