  We numerically study quenches from a fully ordered state to the ferromagnetic
regime of the chiral $\mathbb{Z}_3$ clock model, where the physics can be
understood in terms of sparse domain walls of six flavors. As in the previously
studied models, the spread of entangled domain wall pairs generated by the
quench lead to a linear growth of entropy with time, upto a time $\ell/2v_g$ in
size-$\ell$ subsystems in the bulk where $v_g$ is the maximal group velocity of
domain walls. In small subsystems located in the bulk, the entropy continues to
further grow towards $\ln 3$, as domain walls traverse the subsystem and
increment the population of the two oppositely ordered states, restoring the
$\mathbb{Z}_3$ symmetry. The latter growth in entropy is seen also in small
subsystems near an open boundary in a non-chiral clock model. In contrast to
this, in the case of the chiral model, the entropy of small subsystems near an
open boundary saturates. We rationalize the difference in behavior in terms of
qualitatively different scattering properties of domain walls at the open
boundary in the chiral model. We also present empirical results for entropy
growth, correlation spread, and energies of longitudinal-field-induced bound
states of domain wall pairs in the chiral model.
