Irreversibilities and efficiency at maximum power of heat engines: The illustrative case of a thermoelectric generator

Energy conversion efficiency at maximum output power, which embodies the essential characteristics of heat engines, is the main focus of the present work. The so-called Curzon and Ahlborn efficiency eta(CA) is commonly believed to be an absolute reference for real heat engines; however, a different but general expression for the case of stochastic heat engines, eta(SS), was recently found and then extended to low-dissipation engines. The discrepancy between eta(CA) and eta(SS) is here analyzed considering different irreversibility sources of heat engines, of both internal and external types. To this end, we choose a thermoelectric generator operating in the strong-coupling regime as a physical system to qualitatively and quantitatively study the impact of the nature of irreversibility on the efficiency at maximum output power. In the limit of pure external dissipation, we obtain eta(CA), while eta(SS) corresponds to the case of pure internal dissipation. A continuous transition between from one extreme to the other, which may be operated by tuning the different sources of irreversibility, also is evidenced.