  The problem of factorization of a nonextensive probability distribution is
discussed. It is shown that, in general, the correlation energy between the
correlated subsystems in the canonical composite system can not 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 in the
framework of the Incomplete Statistical Mechanics (ISM).

Statistical Mechanics