  We consider the annealing dynamics of a one-dimensional Ising ferromagnet
induced by a temperature quench in finite time. In the limit of slow cooling,
the asymptotic two-point correlator is analytically found under Glauber
dynamics, and the distribution of the number of kinks in the final state is
shown to be consistent with a Poissonian distribution. The mean kink number,
the variance, and the third centered moment take the same value and obey a
universal power-law scaling with the quench time in which the temperature is
varied. The universal power-law scaling of cumulants is corroborated by
numerical simulations based on Glauber dynamics for moderate cooling times away
from the asymptotic limit, when the kink-number distribution takes a binomial
form. We analyze the relation of these results to physics beyond the
Kibble-Zurek mechanism for critical dynamics, using the kink number
distribution to assess adiabaticity and its breakdown. We consider linear,
nonlinear, and exponential cooling schedules, among which the latter provides
the most efficient shortcuts to cooling in a given quench time. The non-thermal
behavior of the final state is established by considering the trace norm
distance to a canonical Gibbs state.
