When the free energy of similar but distinct molecule-sized objects is plotted against the temperature at which their energy and entropy contributions cancel, a highly significant linear dependence results from which the degree of similarity between the distinctly different members within the group of objects can be quantified and a relationship between energy and entropy is derived. This energy-entropy relationship entirely reflects the mathematical structure of thermodynamic equations, is in this sense fundamental and therefore does probably not dependent on material nor scale. The energy-entropy relationship is likely to be of general interest in molecular biology, population biology, synthetic biology, biophysics, chemical thermodynamics, systems chemistry and physics, most notably in particle physics and cosmology. In physics we predict a consistent and perhaps testable way of classifying micro black holes, to be generated in future Large Hadron Collider experiments, by their gravitational energy and area entropy.