  Voltage fluctuations generated in a hot resistor can cause extraction of heat
from a colder normal metal electrode of a hybrid tunnel junction between a
normal metal and a superconductor. We extend the analysis presented in [Phys.
Rev. Lett. 98, 210604 (2007)] of this heat rectifying system, bearing
resemblance to a Maxwell's demon. Explicit analytic calculations show that the
entropy of the total system is always increasing. We then consider a single
electron transistor configuration with two hybrid junctions in series, and show
how the cooling is influenced by charging effects. We analyze also the cooling
effect from nonequilibrium fluctuations instead of thermal noise, focusing on
the shot noise generated in another tunnel junction. We conclude by discussing
limitations for an experimental observation of the effect.
