Thermodynamic circuits: Association of thermoelectric converters in stationary nonequilibrium

Following up on the recently published circuit theory for thermodynamic devices, we consider networks of thermoelectric converters (TECs) in stationary nonequilibrium. Assuming constant thermoelectric properties, the integration over a finite thickness of the linear local response of the thermoelectric material yields the nonlinear current-force characteristics. We show how to derive a choice of nonequilibrium conductance matrix summarizing the current-force characteristics for all 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 (parallel) association of two TECs using the laws of resistance (conductance) matrix addition. For TECs in series, we find current-dependent boundary conditions for each subdevice. 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.