ABSTRACT
A single condensate partition function in the canonical ensemble of the one-dimensional Gross-Pitaevskii equation has been used to construct the partition function of N noninteracting condensates. In this paper, we employed the appropriate transformation in order to make the partition function of a single condensate to be an extensive quantity by introducing a harmonic volume as the inverse cube of the average geometric trapping frequency. We found that some expressions of the thermodynamic quantities must be corrected to keep the consistency of the thermodynamic expressions based on the Gibbs paradox in the statistical mechanics. This only can be done if a set of condensates is considered as the indistinguishable macroscopic quantum oscillators with a weak nonlinearity instead of the distinguishable ones.
