Maxwell's Conjecture of the Demon creating a Temperature Difference is False

We argue that Maxwell's demon is incapable of creating a nonzero temperature difference. Hence, it does not destroy equilibrium and the second law is never at risk, contrary to the claim by Maxwell and accepted by many. It is therefore remarkable that despite this, the demon paradox has been a valuable source of new ideas. We use two independent arguments, one using classical equilibrium thermodynamics by extending Brillouin's approach, and the other one using equilibrium statistical mechanics and the central limit theorem.