  We analyze a simple implementation of an absorption refrigerator, a system
that requires heat and not work to achieve refrigeration, based on two Coulomb
coupled single-electron systems. We analytically determine the general
condition to achieve cooling-by-heating, and we determine the system parameters
that simultaneously maximize the cooling power and cooling coefficient of
performance (COP) finding that the system displays a particularly simple COP
that can reach Carnot's upper limit. We also find that the cooling power can be
indirectly determined by measuring a charge current. Analyzing the system as an
autonomous Maxwell demon, we find that the highest efficiencies for information
creation and consumption can be achieved, and we relate the COP to these
efficiencies. Finally, we propose two possible experimental setups based on
quantum dots or metallic islands that implement the non-trivial cooling
condition. Using realistic parameters, we show that these systems, which
resemble existing experimental setups, can develop an observable cooling power.
