Can Two Particle-in-a-Box Systems Interact to Affect Entropy?

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WombatWithANuke
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It is interesting to consider why sufficiently slow work does not tend to increase entropy. We can model atoms as a collection of quantum particle-in-a-box’s; Compression work will tend to squeeze the size of these quantum boxes, reducing L.

Now, suppose instead that you left this quantum particle-in-a-box next to a second “hot” particle-in-abox; What effect would this have on the energy states of the original particle-in-a-box? What effect would this have on what states the particle can inhabit? What effect does this have on the entropy?

My thought for the answer is that the hot particle-in-a-box will loose energy giving it to the original particle-in-a-box which will increase the entropy and this would cause the particle to inhabit energy levels higher than ground state.
 

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What you wrote is basically correct, but I do have to say that I fail to see the point.
 
I realize I didn't really add a point to the post haha, this is a problem from homework that I wanted to make sure I was understanding correctly. Because I did posted to another forum and they seemed to think that the original particle-in-a-box would decrease in energy and the entropy would decrease but that didn't make sense to me because the original particle-in-a-box already seemed to be in the ground state. So it couldn't loose more energy. Is my reasoning correct?