Thermodynamic Circuits: Association of thermoelectric converters in stationary non-equilibrium

Following up on the recently published circuit theory for thermodynamic devices, we consider networks of Thermo-Electric Converters (TECs) in stationary non-equilibrium. Assuming constant thermoelectric properties, the integration over a finite thickness of the linear local response of the thermoelectric material yields the non-linear current-force characteristics. We show how to derive a choice of nonequilibrium conductance matrix summarizing the current-force characteristics for every available sets of currents and forces. This problem has infinitely many solutions if one considers only thermodynamic constraints. Each solution differs, among others, by the coupling between the currents. Then, we determine the current-force characteristics of the serial (respectively parallel) association of two TECs using the laws of resistance (respectively conductance) matrix addition. For TECs in series, we find current-dependent boundary conditions for each sub-device. Since currents derive from composite potentials, we also associate the derivability and continuity of these potentials at the interfaces with conditions on thermoelectric coefficients. For TECs in parallel, we discuss the possibility of loop currents that are forbidden for the serial association.