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We use Floquet formalism to study fluctuations in periodically modulatedcontinuous quantum thermal machines. We present a generic theory for suchmachines, followed by specific examples of sinusoidal, optimal, and circularmodulations respectively. The thermodynamic uncertainty relations (TUR) holdfor all modulations considered. Interestingly, in the case of sinusoidalmodulation, the TUR ratio assumes a minimum at the heat engine to refrigeratortransition point, while the Chopped Random Basis (CRAB) optimization protocolallows us to keep the ratio small for a wide range of modulation frequencies.Furthermore, our numerical analysis suggests that TUR can show signatures ofheat engine to refrigerator transition, for more generic modulation schemes. Wealso study bounds in fluctuations in the efficiencies of such machines; ourresults indicate that fluctuations in efficiencies are bounded from above for arefrigerator, and from below for an engine. Overall, this study emphasizes thecrucial role played by different modulation schemes in designing practicalquantum thermal machines.

Precision bound and optimal control in periodically modulated continuous quantum thermal machines