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Several authors have shown that dissipative thermal cycle models based onFinite-Time Thermodynamics exhibit loop-shaped curves of power output versusefficiency, such as it occurs with actual dissipative thermal engines. Withinthe context of First-Order Irreversible Thermodynamics (FOIT), in this work weshow that for an energy converter consisting of two coupled fluxes it is alsopossible to find loop-shaped curves of both power output and the so-calledecological function against efficiency. In a previous work Stucki [J.W. Stucki,Eur. J. Biochem. vol. 109, 269 (1980)] used a FOIT-approach to describe themodes of thermodynamic performance of oxidative phosphorylation involved inATP-synthesis within mithochondrias. In that work the author did not use thementioned loop-shaped curves and he proposed that oxidative phosphorylationoperates in a steady state simultaneously at minimum entropy production andmaximum efficiency, by means of a conductance matching condition betweenextreme states of zero and infinite conductances respectively. In the presentwork we show that all Stucki's results about the oxidative phosphorylationenergetics can be obtained without the so-called conductance matchingcondition. On the other hand, we also show that the minimum entropy productionstate implies both null power output and efficiency and therefore this state isnot fulfilled by the oxidative phosphorylation performance. Our results suggestthat actual efficiency values of oxidative phosphorylation performance arebetter described by a mode of operation consisting in the simultaneousmaximization of the so-called ecological function and the efficiency.

A first--order irreversible thermodynamic approach to a simple energy converter