The current consensus is that Maxwell's Demon does not violate the second law of thermodynamics, because the demon creates order in the box at the expense of creating disorder in the form of information.
Now, let’s assume that we are working with a purely deterministic classical newtonian physical system (for simplicity). Let us also assume that conventional entropy=information entropy. The demon does its job sorting molecules, and stores the information as an “information book” in an “entropy library”. The demon is so proud of its work, that it decides to sort more molecules in more boxes. Of course, this causes the demon to have to store more “books” in the “library”. Suppose one day the demon takes a break from sorting molecules and decides to take a look at the “books” in the “library”. Upon examination of the “library”, the demon realizes that two “books” in particular are redundant. That is, they can be more “ordered” or less “dissipated” if they are “fused” together. Akin to computer data compression, the demon “fuses” the two “books” together, and gets less information (entropy), and now has more concentrated energy, and less entropy.
The moral of the story is that it appears that if the demon has enough high entropy information, and finds two amounts of information that fit together just right, the demon could “fuse” the two pieces of information together (akin to hitting two billiard balls in just the right way to concentrate their velocity into just one billiard ball).
The question I have then, is in this extension to Maxwell’s Demon and information entropy, did the thought experiment violate the second law of thermodynamics? Is there a solution to this proposed violation? Have I showed that entropy is better described as information? And most importantly, if I did not violate the second law of thermodynamics, how will Loschmidt’s Paradox be solved?