  We introduce a classification scheme for the generators of bosonic open
Gaussian dynamics, providing instructive diagrams description for each type of
dynamics. Using this classification, we discuss the consequences of imposing
complete positivity on Gaussian dynamics. In particular, we show that
non-symplectic operations must be active to allow for complete positivity. In
addition, non-symplectic operations can, in fact, conserve the volume of phase
space only if the restriction of complete positivity is lifted. We then discuss
the implications for the relationship between information and energy flows in
open quantum mechanics.
