Accurate calculation of three-body depletion interactions

We compute three-body depletion interactions in a hard-sphere mixture within the framework of density-functional theory and by considering the infinite dilution limit of the functional. The results look very accurate and show three-body interactions much smaller than the pair depletion ones, revealing that these are strongly influenced by correlations and have a decay length similar to the two-body depletion potential. The results are compared with the predictions of the Asakura-Oosawa model for the triplet interactions.