Relevant distance between two different instances of the same potential energy in protein folding

In the context of complex systems and, particularly, of protein folding, a physically meaningful distance is defined which allows to make useful statistical statements about the way in which energy differences are modified when two different instances of the same potential-energy function are used. When the two instances arise from the fact that different algorithms or different approximations are used, the distance herein defined may be used to evaluate the relative accuracy of the two methods. When the difference is due to a change in the free parameters of which the potential depends on, the distance can be used to quantify, in each region of parameter space, the robustness of the modeling to such a change and this, in turn, may be used to assess the significance of a parameters' fit. Both cases are illustrated with a practical example: the study of the Poisson-based solvation energy in the Trp-Cage protein (PDB code 1L2Y).