Nonextensibility of energy in Tsallis' statistics and the zeroth law of thermodynamics

Two important problems existing in Tsallis' statistics are investigated, where one is whether energy is extensive or not, and the other is whether it is necessary to introduce the so-called generalized zeroth law of thermodynamics or not. The results obtained show clearly that like entropy, energy is also nonextensive in Tsallis' statistics, and that the zeroth law of thermodynamics has been implicitly used in Tsallis' statistics since 1988. Moreover, it is expounded that the standard energy additivity rule adopted by a great number of researchers is not suitable in Tsallis' statistics, because it not only violates the law of energy conservation but also its corollary is in contradiction with the zeroth law of thermodynamics.