  Several authors have shown that dissipative thermal cycle models based on
Finite-Time Thermodynamics exhibit loop-shaped curves of power output versus
efficiency, such as it occurs with actual dissipative thermal engines. Within
the context of First-Order Irreversible Thermodynamics (FOIT), in this work we
show that for an energy converter consisting of two coupled fluxes it is also
possible to find loop-shaped curves of both power output and the so-called
ecological function against efficiency. In a previous work Stucki [J.W. Stucki,
Eur. J. Biochem. vol. 109, 269 (1980)] used a FOIT-approach to describe the
modes of thermodynamic performance of oxidative phosphorylation involved in
ATP-synthesis within mithochondrias. In that work the author did not use the
mentioned loop-shaped curves and he proposed that oxidative phosphorylation
operates in a steady state simultaneously at minimum entropy production and
maximum efficiency, by means of a conductance matching condition between
extreme states of zero and infinite conductances respectively. In the present
work we show that all Stucki's results about the oxidative phosphorylation
energetics can be obtained without the so-called conductance matching
condition. On the other hand, we also show that the minimum entropy production
state implies both null power output and efficiency and therefore this state is
not fulfilled by the oxidative phosphorylation performance. Our results suggest
that actual efficiency values of oxidative phosphorylation performance are
better described by a mode of operation consisting in the simultaneous
maximization of the so-called ecological function and the efficiency.
