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    Balancing power, efficiency, and constancy under broken time-reversal symmetry

    Ousi Pan1, Zhiqiang Fan1, Shunjie Zhang1, Liwei Chen2, Jincan Chen1, and Shanhe Su1,*

    • 1Department of Physics, Xiamen University, Xiamen, Fujian 361005, China
    • 2School of Mechanic and Electronic Engineering, Sanming University, Sanming, Xiamen, Fujian 365000, China

    • *Contact author: sushanhe@xmu.edu.cn

    Phys. Rev. E 113, 064117 – Published 8 June, 2026

    DOI: https://doi.org/10.1103/skkv-gqxl

    Abstract

    We derive general trade-off relations between the power, efficiency, and constancy for two-terminal thermoelectric systems in the linear-response regime. Constancy, which quantifies the steadiness of the heat engine, is measured by its fluctuations. The bounds of the efficiency, power, and fluctuations are valid even when time-reversal symmetry is broken, revealing how such a symmetry breaking alters the fundamental constraints on steady-state energy conversion. Our results extend and refine previously established universal trade-offs, offering deeper insight into the performance limits in nonequilibrium thermodynamics. Guided by this bound, heat engines with broken time-reversal symmetry can be operated at near Carnot efficiency while maintaining finite power output and fluctuations, enabling them to outperform their traditional counterparts.

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