The Galilean composition law of velocities within Newtonian mechanics is additive. But, in order to unify mechanics with Maxwell electromagnetism, Einstein adopted the Lorentz space-time transformation as the primary mathematical-physical goal to be satisfied. It resulted the well known, nonadditive, relativistic composition law of velocities. This surely is a small price to pay in order to unify mechanics and electromagnetism, and explain very many experimental facts. Analogously, there is a plethora of analytical, experimental, observational and computational evidences (see Bibliography in http://tsallis.cat.cbpf.br/biblio.htm) which reveals various kinds of violations of Boltzmann-Gibbs (BG) statistical mechanics, including thermodynamics. The adoption of nonadditive entropic functionals which generalize the traditional, additive, BG one enables to satisfy classical thermodynamics: as before, a small price to pay!