For finite ensembles, we estimate the KL divergence, Eq. ( ), numerically using Eq. ( ). In Appendix A, we show how to properly interpret discrete reference weights w (0) α and refined weights w α for ensembles sampled from arbitrary distributions. Thus, all results derived here for continuous distributions also apply to discrete ensembles. We next use that the KL divergence is given by the mean reduced energy differences and relate it to the variance for gentle ensemble refinement.