  We propose and analyze the use of hybrid microwave cavities as quantum heat
engines. A possible realization consists of two macroscopically separated
quantum dot conductors coupled capacitively to the fundamental mode of a
microwave cavity. We demonstrate that an electrical current can be induced in
one conductor through cavity-mediated processes by heating up the other
conductor. The heat engine can reach Carnot efficiency with optimal conversion
of heat to work. When the system delivers the maximum power, the efficiency can
be a large fraction of the Carnot efficiency. The heat engine functions even
with moderate electronic relaxation and dephasing in the quantum dots. We
provide detailed estimates for the electrical current and output power using
realistic parameters.
