  We analyze the performance of slowly driven meso- and micro-scale
refrigerators and heat engines that operate between two thermal baths with
small temperature difference. Using a general scaling argument, we show that
such devices can work arbitrarily close to their Carnot limit only if
heat-leaks between the baths are fully suppressed. Their power output is then
subject to a universal geometric bound that decays quadratically to zero at the
Carnot limit. This bound can be asymptotically saturated in the quasi-static
limit if the driving protocols are suitably optimized and the temperature
difference between the baths goes to zero with the driving frequency. These
results hold under generic conditions for any thermodynamically consistent
dynamics admitting a well-defined adiabatic-response regime and a generalized
Onsager symmetry. For illustration, we work out models of a qubit-refrigerator
and a coherent charge pump operating as a cooling device.

Statistical Mechanics;Quantum Physics