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Low-temperature-differential (LTD) Stirling engines are heat engines that canoperate autonomously with a slight temperature difference betweenlow-temperature heat reservoirs and are thus expected to contribute to asustainable society. A minimal dynamical-system model with only two variableshas been proposed to explain the principle of autonomous rotational motioncaused by temperature differences, and the maximum efficiency of the engine wasformulated [Y. Izumida, Europhys. Lett. 121, 50004 (2018); Phys. Rev. E 102,012142 (2020)]. This paper aims to clarify the coupling effects on thedynamics, power, and thermal efficiency of a pair of weakly coupled LTDStirling engines and formulate the maximum thermal efficiency of the coupledsystem in the quasilinear response regime. We show that the dependence relationbetween the effective frequency difference and the coupling strength ischaracterized by a hysteresis, which comes from different kinds of bifurcationsin the process of increasing and decreasing the value of the coupling strength.Then, by generalizing thermodynamic fluxes and forces and their quasilinearrelations for engines under weak coupling, we show that the coupling improvesthe power exerted against the load torques and the thermal efficiency. Wefurther show that their maximum values are achieved when the engines aresynchronized. Since the thermal efficiency depends on the frequency difference,the dependence of thermal efficiency on the coupling strength is alsocharacterized by a hysteresis. Finally, the load torque that achieves themaximum thermal efficiency of the coupled system is formulated.

Synchronization approach to achieving maximum power and thermal efficiency for weakly-coupled low-temperature-differential Stirling engines