Consider a closed composite system consisting of two simple subsystems.  Previously isolated to any interaction, the two subsystems are now brought into thermal and relations contact, however they are still separated by an entity barrier.  If the entities are individuals this barrier could be a national, cultural, language, or religious boundary.  If the entities are economic organizations this barrier could be a competitive market boundary.

At the new equilibrium the entropy extremum principle requires

where

By the closure condition

therefore

This expression must vanish for independent and arbitrary values of E⁽¹⁾ and E⁽²⁾, therefore

Which of course implies

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