Abstract: The derivations of the most probable distribution are not self-consistent in most statistical physics textbooks since the Stirling’s approximation adopted in the derivations is not valid for systems with few particles. Thus, many attempts are devoted by adding higher Stirling terms to improve the prediction. However, by calculating the ground-state fraction of the ideal Bose system in one-dimensional harmonic trap, we show that the predictions considering the finite size effect are much worse than the predicitons given by the original version without modification. Hence, the finite-size modification to the most probable approximation is not necessary at all.

Key words: the most probable distribution, finite size effect, Bose gas