We propose a quantum thermal machine composed of two nanomechanicalresonators (NMR) (two membranes suspended over a trench in a substrate), placeda few $\mu$m from each other. The quantum thermodynamical cycle is powered bythe Casimir interaction between the resonators and the working fluid is thepolariton resulting from the mixture of the flexural (out-of-plane) vibrations.With the help of piezoelectric cells, we select and sweep the polaritonfrequency cyclically. We calculate the performance of the proposed quantumthermal machines and show that high efficiencies are achieved thanks to (i) thestrong coupling between the resonators and (ii) the large difference betweenthe membrane stiffnesses. Our findings can be of particular importance forapplications in nanomechanical technologies where a sensitive control oftemperature is needed.
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