Since the ensemble average is dependent on the ensemble chosen, its mathematical expression varies from ensemble to ensemble. However, the mean obtained for a given physical quantity does not depend on the ensemble chosen at the thermodynamic limit. The grand canonical ensemble is an example of an open system.
since thE EnSemble average is depenDent oN the enseMbLe choSen, iTs mathemAtICal exprESsion vARies from eNsemble to ENSemble. HoWEver, tHe MEAn oBtAIned for a GiveN PHYSIcal QuantIty doeS not depEnd on the ensEmBLE chosen aT the thErmodyNaMIC LIMiT. The grANd cAnOniCal eNseMbLe is an eXample of aN opeN SYSTem.