  We demonstrate that the relic neutrino asymmetry evolution equation derived
from the quantum kinetic equations (QKEs) reduces to the Boltzmann limit that
is dependent only on the instantaneous neutrino number densities, in the
adiabatic limit in conjunction with sufficient damping. An original physical
and/or geometrical interpretation of the adiabatic approximation is given,
which serves as a convenient visual aid to understanding the sharply
contrasting resonance behaviours exhibited by the neutrino ensemble in opposing
collision regimes. We also present a classical analogue for the evolution of
the difference in $\nu_{\alpha}$ and $\nu_s$ number densities which, in the
Boltzmann limit, is akin to the behaviour of the generic reaction $A
\rightleftharpoons B$ with equal forward and reverse reaction rate constants. A
new characteristic quantity, the matter and collision-affected mixing angle of
the neutrino ensemble, is identified here for the first time. The role of
collisions is revealed to be twofold: (i) to wipe out the inherent
oscillations, and (ii) to equilibrate the $\nu_{\alpha}$ and $\nu_s$ number
densities in the long run. Studies on non-adiabatic evolution and its possible
relation to rapid oscillations in lepton number generation also feature, with
the introduction of an adiabaticity parameter for collision-affected
oscillations.
