Normal metal - superconductor tunnel junction as a Brownian refrigerator

Thermal noise generated by a hot resistor (resistance $R$) can, under proper conditions, catalyze heat removal from a cold normal metal (N) in contact with a superconductor (S) via a tunnel barrier. Such a NIS junction acts as Maxwell's demon, rectifying the heat flow. Upon reversal of the temperature gradient between the resistor and the junction the heat fluxes are reversed: this presents a regime which is not accessible in an ordinary voltage-biased NIS structure. We obtain analytical results for the cooling performance in an idealized high impedance environment, and perform numerical calculations for general $R$. We conclude by assessing the experimental feasibility of the proposed effect.