Abstract: Based on the Euler-MacLaurin formula, the expressions of thermodynamic quantities of a finite-size ideal quantum gas are derived and the effects of the size of the system and the shape of the boundary are revealed. It is shown that the finite-size effects result in several novel characteristics such as the non-extensively of the system, the anisotropy of the pressure, and so on, which are different from those obtained under the thermodynamic limit condition.

Key words: ideal quantum gas, finite-size effect, thermodynamic property