Quantum thermoelectrics in closed circuit with non-equilibrium electrons

The influence of a non-equilibrium classical environment on the parameters of a quantum heat converter in a closed circuit at a given (non-zero) output power is theoretically investigated. It is shown that the non-equilibrium of the electron distribution function in metal terminals contributes to the kinetic coefficients of the linear approximation. Analytical expressions of the Seebeck and Peltier coefficients are obtained, considering the non-equilibrium in the terminals when electric current and heat flow through the system. The influence of non-equilibrium on the theoretical power limit and efficiency of the heat engine at a fixed output power is also determined. Closed-form solutions were obtained for the quantum bound of the heat engine output power and the theoretical limit of the heat conversion efficiency at a given output power in quantum systems with a non-equilibrium environment for certain limited cases. A spectroscopic thermoelectric method for studying quantum systems is proposed.