When I first learned about the depletion interaction, my initial reaction was that it looks very similar to the Casimir effect. On making this remark to the professor, he replied somewhat mystically: "It is the Casimir effect." No further detail was supplied, however.
Nevertheless, it really looks like both problems can be understood in terms of degrees of freedom maximising their positional entropy by reducing the volume of some "forbidden region" between two objects. For the depletion interaction, the fluctuating degrees of freedom are small particles, while in the Casimir effect, these degrees of freedom are long-wavelength modes of the free radiation field. However, a key difference is that in the first case the fluctuations arise thermally, while in the second case they are unavoidable quantum fluctuations of the vacuum.
Is it possible to derive the Casimir force between two conducting plates from entropic considerations alone?