a weak relaxation mechanism within the reservoirs will cause the two parts of the circuit to each relax to internal equilibrium (see Fig. \[Fig:Unique\]a). After this one can unambiguously identify the temperature, $T_i$, internal energy $Q_i$ and Clausius entropy $S_i=Q_i\big/ T_i$ of the two parts of the circuit (for $i=L,R$). Since the reservoirs are large, we assume $T_i = T_i^{(0)}$.

Thus, we can unambiguously say that the heat-current out of reservoir $i$ [*averaged*]{} over the time $t_{\rm expt}$ is $$\begin{aligned}
\langle J_i \rangle = \big (Q^{(0)}_i - Q_i \big) \big/ t_{\rm expt}.\end{aligned}$$ For the above thermocouple, we treat the currents for each thermoelectric separately, writing the heat current out of reservoir $L$ as $J_L+J_{L'}$, where $J_L$ is the heat current from reservoir $L$ into the lower thermoelectric in Fig. \[Fig:thermocouple\] (the filled circle), and $J_{L'}$ is the heat current from reservoir $L$ into the upper thermoelectric in Fig. \[Fig:thermocouple\] (the open circle). Treating each thermoelectric separately is convenient, and also allows one to generalize the results to “thermopiles”, which contain hundreds of thermoelectrics arranged so that they are electrically in series, but thermally in parallel.

The average rate of change of entropy in the circuit is $\langle \dot S_{\rm circuit} 