  We study the evolution of a cosmological baryon asymmetry produced via
leptogenesis by means of the full classical Boltzmann equations, without the
assumption of kinetic equilibrium and including all quantum statistical
factors. Beginning with the full mode equations we derive the usual equations
of motion for the right-handed neutrino number density and integrated lepton
asymmetry, and show explicitly the impact of each assumption on these
quantities. For the first time, we investigate also the effects of scattering
of the right-handed neutrino with the top quark to leading order in the Yukawa
couplings by means of the full Boltzmann equations. We find that in our full
Boltzmann treatment the final lepton asymmetry can be suppressed by as much as
a factor of 1.5 in the weak wash-out regime (K<1), compared to the usual
integrated approach which assumes kinetic equilibrium and neglects quantum
statistics. This suppression is in contrast with the enhancement seen in some
previous studies that considered only decay and inverse decay of the
right-handed neutrino. However, this suppression quickly decreases as we
increase K. In the strong wash-out regime (K>1), the full Boltzmann treatment
and the integrated approach give nearly identical final lepton asymmetries
(within 10 % of each other at K>3). Finally, we show that the opposing effects
of quantum statistics on decays/inverse decays and the scattering processes
tend to reduce the net importance of scattering on leptogenesis in the full
treatment compared to the integrated approach.
