Fourth statistical ensemble for the Bose-Einstein condensate

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