the large mass absorber, $G_{ta}$, is still 50$\times$ smaller than the thermal conductance between the TES and the bath via the direct electronic coupling of the Au wirebond, $G_{tb}$ ([*c*f.]{} Table. \[tab:PhononDet\]). This is because the W electronic system (sensor) and the phonon system of the TES and absorber almost completely decouple at very low temperatures since the thermal power flow scales as $T^{5}$.

From a modeling perspective, the primary consequence is that any realistic device simulation requires separate thermal DOF for the absorber, $T_{a}$, and the TES, $T_{t}$, in addition to modeling the current flowing through the TES $I_{t}$ which will be measured through an inductively coupled SQUID. Thus in a way similar to CRESST [@CRESST_1995_ProbstModel], we will model the system as 3 coupled non-linear differential equations

$$\begin{split}
L \frac{dI_{t}}{dt}           &= V_{b} - I_{t} \left( R_{l}+R_{t}(T_{t},I_{t}) \right) + \delta V\\
C_{t}  \frac{dT_{t}}{dt}  &= I_{t}^{2}R_{t}(T_{t},I_{t}) - P_{tb}(T_{t},T_{b})- P_{ta}(T_{t},T_{a})  + Q + \delta P_{t}\\
C_{a} \frac{dT_{a}}{dt} &= - P_{ab}(T_{a},T_{b}) + P_{ta}(T_{t},T_{a}) + \delta P_{a}
\end{split}
\label{eq:NonLin_dyn}$$

where $\delta V$ is a small voltage-bias excitation on top of the DC voltage-bias $V_{b}$ that we will use to model Johnson noise as well as the small signal dynamics of the detector. Likewise, $\delta 