thermodynamics - Maxwell demon : how can the demon move the door without doing any work ?

Here is something that I never understood about Maxwell's demon paradox : in order to contradict the second law of thermodynamics, the demon must open and close the door without doing any work... But how is that possible ?

I know it is just a thought experiment but still, as I see it, it just shows (by contraposition) that, if you assume the second principle to hold true, then there cannot exist a device that will open and close the door in this way without doing any actual work (for instance, there will necessarily be some friction or whatever which will creates some work..)

Seeing things this way there is no paradox and it only states, as a corollary of the second law, that such a demon cannot exist...

Obviously, I am missing something here since there seems to be much more to this thought experiment than that... I would be extremely grateful if someone would take the time to explain to me where I am mistaken ! :)

Thanks !

Answer

The idea is that there is no fundamental physical limit to how little energy is required to open and close the door. So you can make it arbitrarily small, and if you make it small enough, the demon still contradicts the Second Law of Thermodynamics.

This definitely isn't apparent at first sight, but I believe this is one of the first things people checked in attempts to resolve the paradox. If it had been this easy to resolve, it wouldn't have stayed open for as long as it did.

The rather non-intuitive resolution of the Maxwell demon paradox is that you need $(ln 2) k T$ energy to erase each bit of information from the demon's memory. See Landauer's Principle and this stack-exchange question.