Since the Boltzmann constant k B = R / N A , where N A is the Avogadro constant, and the number of molecules N = n N A , we recover the thermodynamic expression for the mixing of two ideal gases, Δ Δ S mix = − − n R [ x 1 ln ⁡ ⁡ x 1 + x 2 ln ⁡ ⁡ x 2 ]