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It is typically assumed, without justification, that a weak coupling betweena system and a bath is a necessary condition for the equivalence of a canonicalensemble 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 acoupled composite-spin system. Our results show that the spin coupling strengthcan be as large as the level spacing of the system, indicating that the weakcoupling approximation has a much wider region of validity than usuallyexpected.

Equivalence condition for the canonical and microcanonical ensembles in coupled spin systems