We study the Bose-Einstein condensate (BEG) with a fixed number of par
ticles. On the basis of conventional statistical mechanics we introduc
e the, so called, Maxwell's demon ensemble, where only particle transf
er (without energy exchange) is allowed. We show that this new ensembl
e can be used for the microcanonical description of the system. We app
ly our formalism to the case of BEC in a harmonic trap and give the an
alytic expressions for the ground state fluctuations. We compare these
expressions with the exact numerical results obtained for relatively
small condensates.