The Tsallis statistical distribution in a completely open system

► We prove that an extensive or intensive quantity is not pure in a long-range interacting system. ► The “phase rule” of extensive statistical mechanics therefore does not hold. ► Partition functions are not restricted by the so-called intensive quantities. ► We deduce the statistical distribution of a completely open system and formulas for its thermodynamical quantities. ► The results are not limited to small systems.