But we could certainly squeeze more entropy into the box if we wanted to; all we would have to do is add more and more molecules. If we were worried that the molecules took up a certain amount of space, so there was some maximum number we could squeeze into the box, we might be clever and consider a box full of photons (light particles) instead of gas molecules. Photons can be piled on top of one another without limit, so we should be able to have as many photons in the box as we wish. From that point of view, the answer seems to be that we can fit an infinite (or at least arbitrarily large)
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