We show here that the concepts of nonextensive thermodynamics (NET), described previously (J. Phys. Chem. B, 2004, 108, 18980) and applied to redox behavior of nanoparticles (J. Phys. Chem. C, 2008, 112, 12116) can be used to express by a power law the variations to the electrochemical kinetics of nanoparticles and in particular to voltammetry. We proposed here a generalization of Plieth's relationship for non-spherical aggregates by assuming that the interface between the particle and its environment is fuzzy. Thus, the relations of non-extensive thermodynamics can quantitatively account for the displacements of electro-oxidation potentials of metal nanoparticles deposited on electrodes, according to their measured size. Our approach also permits to formally justify the stability of the particles may increase as their size decreases, (τ<0). This is usually found when the aggregates are in close contact with a matrix (in the case, for example, of embedded particles).