Some features of nonadiabatic electron heat pumps are studied and connected to general questions of quantum cooling. Inelastic reflection is shown to contribute to heating if the external driving signal is time-symmetric. The quantum of cooling power, $pi^2 k_B^2 T^2/6h$, is shown to be an upper limit to the cooling rate per transport channel in the presence of an arbitrary driving signal. The quantum limit to bulk atom cooling is also discussed. Within the electron tunneling limit, it is shown that electron cooling still occurs if the coherent ac source is replaced by a sufficiently hot thermal bath. A comparison with related refrigeration setups is presented.
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