Nonextensive distribution and factorization of the joint probability

The problem of factorization of Tsallisʹ nonextensive probability distribution is discussed in a general way. It is shown that the correlation energy between the correlated subsystems in the canonical composite system cannot be neglected even in the thermodynamic limit. In consequence, the factorization approximation should be employed carefully according to different systems. It is also shown that the zeroth law of thermodynamics can be established without factorization approximation in the framework of the incomplete statistical mechanics.