  The nonequilibrium description of quantum systems requires, for more than two
or three particles, the use of a reduced description to be numerically
tractable. Two possible approaches are based on either reduced density matrices
or nonequilibrium Green's functions (NEGF). Both concepts are formulated in
terms of hierarchies of coupled equations---the
Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for the reduced density
operators and the Martin-Schwinger-hierarchy (MS) for the Green's functions,
respectively. In both cases, similar approximations are introduced to decouple
the hierarchy, yet still many questions regarding the correspondence of both
approaches remain open.
