Question: Show that the partition function Z(1 + 2) of two independent systems 1 and 2 in thermal contact at a common temperature is equal

Show that the partition function Z(1 + 2) of two independent systems 1 and 2 in thermal contact at a common temperature τ is equal to the product of the partition functions of the separate systems:
Z(1 + 2) = Z(1)Z(2)

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