Abstract: Tsallis＇ statistics is simply introduced in the nonextensive statistical mechanics. Complete gases is discussed by using the Tsallis＇ statistics. The statistical distributions for completely open systems are simply derived by the Shannon＇ s entropy contained a nonextensive constant of entropy and Tsallis＇ entropy for the nonextensive statistical mechanics.

Key words: nonextensive statistical mechanics, entropy, completely open system, statistical distribution