Abstract
The following problem is investigated: How large must an ideal Bose-system be to allow for the approximation of the finite system free energy by the thermodynamic limit. The obvious condition that the energy separations between the single-particle states must be small compared to kT is necessary but is not sufficient near the critical concentration. Instead, for this case additional stronger conditions apply due to the singularity of the thermodynamic free energy at the critical point which is caused by contributions of the lowest-energy single-particle states. These conditions are derived and the relevancy of the results is emphasized for a generalized theory of metastability in co-operative systems.
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