How Many Maxwell’s Demons, and Where?

Abstract

Maxwell’s demon has been conceived as a tool for challenging the law of entropy increase. Several resolutions of the paradox have been proposed, making it clear that the demon does not violate the second law of thermodynamics. Nevertheless, since recent experiments come close to realizing some variants of Maxwell’s demon, it is interesting to revisit it. In this article we first address two questions, left unnoticed despite many years of intensive study: (1) on which side of the door should the demon be located when the door is shut? and (2) how is kinetic energy exchanged between the two compartments due to the demon’s sorting? We propose a simple setting which is more realistic than the current versions, in which the demon monitors and accesses both sides of the partition, so as to enable the sorting task. Next we study the impact of this sorting on the molecular kinetic energy exchanges. We show that the temperature difference between compartments grows till the cold part of the gas approaches 0 K. We then emphasize that this setting yields to the familiar resolution of the paradox. In the last part we derive the expression of the average rate of energy flow between the two compartments of the system, based on the new setting proposed.