  It is typically assumed, without justification, that a weak coupling between
a system and a bath is a necessary condition for the equivalence of a canonical
ensemble and a microcanonical ensemble. For instance, in a canonical ensemble,
temperature emerges if the system and the bath are uncoupled or weakly coupled.
We investigate the validity region of this weak coupling approximation, using a
coupled composite-spin system. Our results show that the spin coupling strength
can be as large as the level spacing of the system, indicating that the weak
coupling approximation has a much wider region of validity than usually
expected.
