On the conversion of the confined ideal gas distribution between the canonical and the grand canonical ensembles

Abstract

In this short communication, we show that the analytical solution for the single-particle density of a confined ideal gas within the grand canonical ensemble can be derived from its correlate within the canonical ensemble, without resorting to the Density Functional Theory, avoiding the inherent complications in the transformation between these ensembles. Framing the adsorption phenomenon as a phase equilibrium problem, we then show that both distributions are equal at the same thermodynamic state.