The closed time- path formalism is a powerful Green's function formulation to describe non- equilibrium phenomena in field theory and it leads to a complete non- equilibrium quantum kinetic theory. We make use of this formalism to write down the set of quantum Boltzmann equations relevant for leptogenesis. They manifest memory effects and off-shell corrections. In particular, memory effects lead to a time- dependent CP asymmetry whose value at a given instant of time depends upon the previous history of the system. This result is particularly relevant when the asymmetry is generated by the decays of nearly mass- degenerate heavy states, as in resonant or soft leptogenesis.
