A composition of different $q$ nonextensive systems with the normalized expectation based on escort probability

This is a study of composition rule and temperature definition for nonextensive systems containing different $q$ subsystems. The physical meaning of the multiplier $\beta$ associated with the energy expectation in the optimization of Tsallis entropy is investigated for the formalism with normalized expectation given by escort probability. This study is carried out for two possible cases: the case of the approximation of additive energy; and the case of nonadditive energy prescribed by an entropy composition rule for different $q$ systems.