From local force-flux relationships to internal dissipations and their impact on heat engine performance: The illustrative case of a thermoelectric generator

We present an in-depth analysis of the sometimes understated role of the principle of energy conservation in linear irreversible thermodynamics. Our case study is that of a thermoelectric generator (TEG), which is a heat engine of choice in irreversible thermodynamics, owing to the coupling between the electrical and heat fluxes. We show why Onsager's reciprocal relations must be considered locally and how internal dissipative processes emerge from the extension of these relations to a global scale: the linear behavior of a heat engine at the local scale is associated with a dissipation process that must partake in the global energy balance. We discuss the consequences of internal dissipations on the so-called efficiency at maximum power, in the light of our comparative analyses of exoreversibility and endoreversibility on the one hand, and of two classes of heat engines, autonomous and periodically-driven, on the other hand. Finally, basing our analysis on energy conservation, we also discuss recent works which claim the possibility to overcome the traditional boundaries on efficiency imposed by finite-time thermodynamics in thermoelectric systems with broken time-reversal symmetry; this we do by introducing a "thermal" thermopower and an "electrical" thermopower which permits an analysis of the thermoelectric response of the TEG considering a possible dissymmetry between the electrical/thermal and the thermal/electrical couplings.