A new physics approach is presented to evaluate the theoretical transmutation potential of different nuclear power systems (standard or advanced fission reactors and hybrid accelerator/sub-critical blankets). The nuclei to be transmuted are the transuranium (or transplutonium) isotopes produced in the irradiation of naturally occurring fuels (uranium or thorium) and the fission product isotopes. The analysis is based on an evaluation of neutronic constraints on the transmutation rates integrated over the life of the nuclide families, taking into account the overall neutron balance of the system being considered. This method allows a comparison of the potential of different systems and establishes physics limitations, particularly in the field of fission product transmutation.