Thermodynamic Circuits 2: Nonequilibrium conductance matrix for a thermoelectric converter

Abstract

In the linear regime, Onsager's response matrix provides the coupling between heat and charge currents crossing a section of thermoelectric materials of infinitesimal thickness. Integrating this response over the finite thickness of a one-dimensional Thermoelectric Converter (TEC) leads to quadratic heat-force characteristics (Joule's law) and linear current-voltage characteristics (Ohm's law). However, these non-linear characteristic equations are not matrix relation anymore. This prevents from determining the currents degree of coupling, albeit its central role for optimizing energy conversion. Based on current conservation laws, i.e., the linear dependence between internal physical currents (crossing a section of material) or between external ones (exchanged with the environment), we distinguish two relevant basis of physical and fundamental currents. For those, we define non-equilibrium conductance matrices providing the current-force relations of a TEC in any convenient basis. In doing so, we introduce a degree of coupling between heat and charge currents, in line with the work of Kedem and Caplan but beyond weakly irreversible thermodynamics. This demonstrates by example that non-equilibrium conductance matrices constitute effective models for driven systems, as Onsager response matrices do in the linear regime. The sequel papers of this series focus on associating systems modeled in such way.