The results presented here can be generalized to non-Boltzmann distributions and are thus valid for the general class of Bayesian/MaxEnt approaches for ill-defined inverse problems. In such cases, we take advantage of the fact that the energy entering Boltzmann's distribution corresponds to Shannon's information content h(x) = -ln p(x) for arbitrary probability distributions p(x). Consequently, the difference in energy corresponds to a difference in information, ∆h(x) = ln[p(x)/q(x)], Eq. ( ). Like in gentle ensemble refinement, the KL divergence can be approximated by the variance of this information difference, i.e., S KL ≈ var(∆h)/2, if these differences are small. In general, we express our confidence in the 'natural unit of information' or 'nat', which is numerically equal to k B T for Boltzmann distributions.