Maxwell’s demon, power, and time

Abstract

What rate (Pd) of energy transfer is attainable by a Maxwell’s demon who sorts gas molecules serially; and how much time (td) does it take to achieve a designated temperature difference ΔT across a partition? Two estimates are made, using (i) the energy–time form of Heisenberg’s uncertainty principle and (ii) classical kinetic theory. For a dilute gas, at ∼300 K, the uncertainty principle implies Pd <1.5×10−6 W. If the gas volume is the size of a large room, and ΔT=2 K, then td >103 years. These bounds are loose, but are of interest because this is one of few elementary applications of the energy–time uncertainty principle. With similar assumptions, classical kinetic theory implies much tighter bounds: Pd <10−9 W and td >4×106 years. The kinetic theory approach allows an extension of Brillouin’s demonstration that the second law of thermodynamics cannot be violated by a Maxwell’s demon using light signals.