  We extract the imaginary part of the heavy-quark potential using
classical-statistical simulations of real-time Yang-Mills dynamics in classical
thermal equilibrium. The $r$-dependence of the imaginary part of the potential
is extracted by measuring the temporal decay of Wilson loops of spatial length
$r$. We compare our results to continuum expressions obtained using hard
thermal loop theory and to semi-analytic lattice perturbation theory
calculations using the hard classical loop formalism. We find that, when
plotted as a function of $m_D r$, where $m_D$ is the hard classical loop Debye
mass, the imaginary part of the heavy-quark potential is independent of the
lattice spacing at small $r$ and agrees well with the semi-analytic hard
classical loop result. For large quark-antiquark separations, we quantify the
magnitude of the non-perturbative long-range corrections to the imaginary part
of the heavy-quark potential. We present our results for a wide range of
temperatures, lattice spacings, and lattice volumes. Based on our results, we
extract an estimate of the heavy-quark transport coefficient $\kappa$ from the
short-distance behavior of the classical potential and compare our result with
$\kappa$ obtained using hard thermal loops and hard classical loops. This work
sets the stage for extracting the imaginary part of the heavy-quark potential
in an expanding non-equilibrium Yang Mills plasma.
