The approximation of the KL divergence by the variance, Eq. ( ), holds for arbitrarily shaped distribution functions of the reduced energy differences ∆u (Figure , top). The distribution functions are bimodal for the double-well system, monomodal for the polymer model, and well approximated by Gaussian distributions for Ala 5 . The approximation of the KL divergence by the variance works especially well for the latter, as it is exact for a Gaussian ∆u distribution.