Thermoelectricity - Thermodynamics and applications

Thermoelectricity is an old subject in physics, both in terms of its discoveries and its applications, dating back to the end of the first half of the 19th century, which was also the century of the birth of thermodynamics. However, the theoretical description of thermoelectric phenomena within the framework of non-equilibrium linear thermodynamics did not emerge until much later, with the work of Lars Onsager in 1931 and Herbert Callen from 1947 onwards. It is interesting to note that the signatures of thermoelectric effects are always the result of couplings: coupling of potentials, temperature and electrochemical potential in the case of the Seebeck effect, in 1821 ; then coupling of heat and electric flux in the case of the Peltier effect in 1834 . However, it wasn't until 1855 that William Thompson, the future Lord Kelvin, took a thermodynamic approach and combined the Seebeck and Peltier effects into a single expression . He then demonstrated the existence of a new effect, the Thomson effect, resulting from the gradient of the Seebeck coefficient. It was then demonstrated that thermal and electrical potentials, as well as the associated fluxes, are coupled by the one and only coupling coefficient, the Seebeck coefficient. The diversity of Seebeck, Peltier or Thomson signatures ultimately reveals only the thermodynamic conditions imposed during the experiment: direct effect in the case of the Seebeck effect, or gradient effect in the case of the Peltier and Thomson effects. It's important to note that irreversibility remains at the heart of these effects, and the unifying character of Thomson's work came up against the impossibility of writing the expression of entropy production as an equality rather than as Clausius' inequality. This difficulty was only resolved in 1931, within the very strict framework of linear irreversible thermodynamics proposed by Lars Onsager . It was on this basis that Herbert Callen developed his description...