We first establish the range of validity for gentle ensemble refinement for the three example systems, as established in subsection II F. The range of validity of the approximation of the KL divergence by the energy uncertainty, Eq. ( ), depends on the system under consideration (Figure ). We find good agreement for decreasing θ values down to (θ, S KL ) ≈ (10, 0.17) for the double-well system; to (θ, S KL ) ≈ (10, 0.26) for the polymer model; and to (θ, S KL ) ≈ (1, 1.43) for Ala 5 . In gentle ensemble refinement, the two definitions of the KL divergence are approximately equivalent, S KL (p||q) ≈ S KL (q||p) [Eq. (34) and Figure ]. The relative residuals of S KL (q||p) and of the approximation by half the energy variance with respect to S KL (p||q) are of similar shape and magnitude but opposite sign (Figure , bottom panels). For all three systems, we have S KL ≲ 1 for θ ≳ 10, which overall delimits the regime of gentle refinement.