  Time reversal symmetry is a fundamental property of many quantum mechanical
systems. The relation between statistical physics and time reversal is subtle
and not all statistical theories conserve this particular symmetry, most
notably hydrodynamic equations and kinetic equations such as the Boltzmann
equation. Here we consider quantum kinetic generalizations of the Boltzmann
equation by using the method of reduced density operators leading to the
quantum generalization of the BBGKY-(Bogolyubov, Born, Green, Kirkwood, Yvon)
hierachy. We demonstrate that all commonly used approximations, including
Vlasov, Hartree-Fock and the non-Markovian generalizations of the Landau,
T-matrix and Lenard-Balescu equations are originally time-reversal invariant,
and we formulate a general criterion for time reversibility of approximations
to the quantum BBGKY-hierarchy. Finally, we illustrate, on the example of the
Born approximation, how irreversibility is introduced into quantum kinetic
theory via the Markov limit, making the connection with the standard Boltzmann
equation. This paper is a complement to paper I [Scharnke {\it et al.},
submitted to J. Math. Phys., arXiv:1612.08033] where time-reversal invariance
of quantum-kinetic equations was analyzed in the frame of the independent
nonequilibrium Green functions formalism.
