Constitutive relation for nonlinear response and universality of efficiency at maximum power for tight-coupling heat engines

We present a unified perspective on nonequilibrium heat engines by generalizing nonlinear irreversible thermodynamics. For tight-coupling heat engines, a generic constitutive relation for nonlinear response accurate up to the quadratic order is derived from the stalling condition and the symmetry argument. By applying this generic nonlinear constitutive relation to finite-time thermodynamics, we obtain the necessary and sufficient condition for the universality of efficiency at maximum power, which states that a tight-coupling heat engine takes the universal efficiency at maximum power up to the quadratic order if and only if either the engine symmetrically interacts with two heat reservoirs or the elementary thermal energy flowing through the engine matches the characteristic energy of the engine. Hence we solve the following paradox: On the one hand, the quadratic term in the universal efficiency at maximum power for tight-coupling heat engines turned out to be a consequence of symmetry [Esposito, Lindenberg, and Van den Broeck, Phys. Rev. Lett. 102, 130602 (2009); Sheng and Tu, Phys. Rev. E 89, 012129 (2014)]; On the other hand, typical heat engines such as the Curzon-Ahlborn endoreversible heat engine [Curzon and Ahlborn, Am. J. Phys. 43, 22 (1975)] and the Feynman ratchet [Tu, J. Phys. A 41, 312003 (2008)] recover the universal efficiency at maximum power regardless of any symmetry.

Figure 1

Refined generic model of a tight-coupling heat engine (reproduced according to Ref. [39]).