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We present a unified perspective on nonequilibrium heat engines bygeneralizing nonlinear irreversible thermodynamics. For tight-coupling heatengines, a generic constitutive relation of nonlinear response accurate up tothe quadratic order is derived from the symmetry argument and the stallcondition. By applying this generic nonlinear constitutive relation tofinite-time thermodynamics, we obtain the necessary and sufficient conditionfor the universality of efficiency at maximum power, which states that atight-coupling heat engine takes the universal efficiency at maximum power upto the quadratic order if and only if either the engine symmetrically interactswith two heat reservoirs or the elementary thermal energy flowing through theengine matches the characteristic energy of the engine. As a result, we solvethe following paradox: On the one hand, the universal quadratic term in theefficiency at maximum power for tight-coupling heat engines proved as aconsequence of symmetry [M. Esposito, K. Lindenberg, and C. Van den Broeck,Phys. Rev. Lett. 102, 130602 (2009); S. Q. Sheng and Z. C. Tu, Phys. Rev. E 89,012129 (2014)]; On the other hand, two typical heat engines including theCurzon-Ahlborn endoreversible heat engine [F. L. Curzon and B. Ahlborn, Am. J.Phys. 43, 22 (1975)] and the Feynman ratchet [Z. C. Tu, J. Phys. A 41, 312003(2008)] recover the universal efficiency at maximum power regardless of anysymmetry.

Constitutive Relation for Nonlinear Response and Universality of Efficiency at Maximum Power for Tight-Coupling Heat Engines