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Though it is a long time since I have read the book I remember that the point of calling it Demon Box refers to a girl who has understood what "Maxwell's demon" is all about, and why Maxwell's thought experiment triggered a philosophical discussion relating to what properties life has. So if the story about the publisher's search for a name holds true there are at least one more explanation. However, the discussion about "Maxwell's Demon" is very high-brow and therefore probably not something which is good for marketing.
I am in need of a term to replace "Maxwell's daemon" discussion. The term needs to emphasize that Maxwell's demon does not exist (even if the Wikipedia article mentions experiments which seem to show that some concentration of energy may be obtained by a one-way wall), but is a thought experiment showing how energy may be extracted from air (gas) where the molecules move with different speeds (but temperature measurement of course show one temperature, low entropy) and that this thought experiment has triggered discussions about whether life (and consciousness) just is a phenomenon in physical matter or whether life creates higher entropy (Earth surface as such is an example of higher entropy obtained - or created - by life).
(TODO: Find the ref. in the book where the hospitalized girl explains the Demon Box)