I discuss the derivation of a single-time quantum transport equation, which includes effects beyond the quasiparticle approximation. I restrict myself to Fermi-systems and use the framework of non-equilibrium real-time Green's functions theory. Ternary correlations are incorporated in the kinetic description via a cluster expansion for the self-energies (e.g., the transport vertex and the width) truncated at the level of three-body scattering amplitudes. A finite temperature/density formulation of the three-body problem is given. Corresponding three-body equations reduce to the well-known Faddeev equations in the vacuum limit. In equilibrium the equations of state contains virial corrections proportional to the third quantum virial coefficient. I also discuss the coherence effects in neutrino pair bremsstrahlung in neutron stars.