Geometric thermodynamic uncertainty relation in a periodically driven thermoelectric heat engine

Thermodynamic uncertainty relation, quantifying a trade-off among average current, the associated fluctuation (precision), and entropy production (cost), has been formulated in nonequilibrium steady state various stochastic systems. Herein, we study thermodynamic relation generic thermoelectric heat engines under periodic control protocol, by uncovering underlying Berry-phase-like contribution. We show that our breaks seminal steady-state results, originating from non-vanishing geometric effect. Furthermore, deriving consequent binding efficiency, power, constancy, prove periodically driven can generally outperform analogies. The general bounds are illustrated an analytically solvable two-terminal single quantum dot engine modulation. Our work provides framework bounding optimizing wide range of thermal machines.