Finite Volume Thermodynamics of an Ideal Gas in a Periodic Box

Abstract

Approach to the thermodynamic limit of a non-relativistic ideal gas in a periodic box is investigated. The single particle wave function obeys twisted boundary condition, $\psi(L)=e^{i\theta}\psi(0)$ for which the free particle spectrum is constructed in terms of the twist angle, $\theta$. The exact density of states is utilized to construct finite-size corrections of thermodynamic observables. Leading finite volume corrections in the free energy do not arise due to the boundary -- its implication for mixing entropy is examined. Finite volume corrections to the average energy, its fluctuations and the pressure are also examined with corrections arising exclusively through the boundary condition. However, the equation of state, the ratio of pressure to energy density, remains unmodified by the boundary.