Why does Maxwell's Demon need to be exorcized?

The standard version of Maxwell's Demon allows for a perpetual motion machine, producing an infinite amount of work from a finite-temperature reservoir. This seems too good to be true, and since nobody has ever successfully built a perpetual motion machine, it is widely believed that these are unlikely to exist.

A number of physicists believe that Maxwell's Demon has been exorcised. This was done using Landauer's principle:

the minimum possible amount of energy required to erase one bit of information is kT ln 2.

In order to operate, the Demon needs to remember which way he sent the molecules. Eventually, his memory becomes full, and he is unable to keep operating. Once he starts erasing his memory, he can no longer reduce the entropy of the system for free.

Viewed in another way, the Demon is simply a heat engine that operates on the difference of temperature between the system and his memory (which has temperature 0).

If a physical process could bring about an energy movement from a colder to a hotter body, with no other change, at the macroscopic thermodynamic level, in the rest of the universe (this what Maxwell's thought-experiment purports to do) then it would mean the 2nd law did not hold universally (in the thermodynamic limit where it becomes a precise statement). However, no one has ever succeeded in proposing a physical process which actually achieves this, so as far as we know the Maxwell daemon is a physical impossibility.

It is good practice to invest intellectual effort in this way, I mean to check that a process ruled out by the 2nd law is indeed not possible, because it helps our understanding to know that the 2nd law does indeed hold. This is important because that law, or descriptive principle, plays such a useful role in many areas of science, especially chemistry.