  We uncover the connection between the Fitness-Complexity algorithm, developed
in the economic complexity field, and the Sinkhorn-Knopp algorithm, widely used
in diverse domains ranging from computer science and mathematics to economics.
Despite minor formal differences between the two methods, both converge to the
same fixed-point solution up to normalization. The discovered connection allows
us to derive a rigorous interpretation of the Fitness and the Complexity
metrics as the potentials of a suitable energy function. Under this
interpretation, high-energy products are unfeasible for low-fitness countries,
which explains why the algorithm is effective at displaying nested patterns in
bipartite networks. We also show that the proposed interpretation reveals the
scale invariance of the Fitness-Complexity algorithm, which has practical
implications for the algorithm's implementation in different datasets. Further,
analysis of empirical trade data under the new perspective reveals three
categories of countries that might benefit from different development
strategies.
