text: Asakura and Oosawa assumed a uniform particle density, which is true in a homogeneous solution. However, if an external potential is applied to a solution, then the uniform particle density is disrupted, making Asakura and Oosawa's assumption invalid. Density functional theory accounts for variations in particle density by using the grand canonical potential. The grand canonical potential, which is a state function for the grand canonical ensemble, is used to calculate the probability density for microscopic states in macroscopic state. When applied to depletion forces, the grand canonical potential calculates the local particle densities in a solution.