On the different formalisms for the transport equations of thermoelectricity: A review

Abstract Researchers in thermoelectricity with backgrounds in non-equilibrium thermodynamics, thermoelectric engineering or condensed-matter physics tend to use different choices of flux densities and generalized forces. These choices are seldom justified from either the dissipation function or the entropy production rate. Because thermoelectric phenomena are a primary focus in several emerging fields, particularly in recent energy-oriented developments, a review of the different formalisms employed is judged timely. A systematic classification of the transport equations is presented here. The requirements on valid transport equations imposed by the invariance of the entropy production are clearly explained. The effective Peltier and Seebeck coefficients, and the thermal conductivity, corresponding to the different choices of flux densities and generalized forces, are identified. Emphasis is made on illustrating the compatibility of apparently disparate formalisms. The advantages and drawbacks of these formalisms are discussed, especially from the point of view of the experimental determination of their thermoelectric coefficients.