across a thermal link between two different temperatures (a non-equilibrium situation) is less than the naively derived equilibrium noise [@McCammon_TES]. Now, estimation of the TFN across $G_{ab}$ is slightly more difficult since we must refer it to the TES and thus $$\begin{split}
S_{P_{t} \, G_{ab}}     &= \left({\frac{\partial I_{t}}{\partial P_{a}}}/\frac{\partial I_{t}}{\partial P_{t}}\right)^2 4k_{b}T_{ao}^{2}G_{ab} {\mathcal{F}}(T_{ao},T_{b},\mbox{diffusive})  \\
                &\sim {\left( \frac{G_{ta,a}}{G_{ta,a}\! + \!G_{ab}}\right)}^{2}
                \frac{1}{1+\omega^{2}/\omega_{ta}^2}
                4k_{b}T_{ao}^{2}G_{ab} {\mathcal{F}}\end{split}
\label{eq:Si-Gab}$$ This noise is subdominant, even below the $\omega_{ta}$ pole since $G_{ab} \ll G_{tb}$ for both CRESST detectors (as well as for our new design).

Next, we estimate our sensitivity to thermal fluctuations between the electronic and phonon systems (i.e. across $G_{ta}$). We must be cognizant that these fluctuations are anti-correlated to conserve energy; if thermal power randomly flows into the phonon system, it must be flowing out of the electronic system and vice-versa. Thus, our sensitivity is $$\begin{split}
S_{P_{t} \, G_{ta}}     &= \left( \frac{\frac{\partial I_{t}}{\partial P_{t}} - \frac{\partial I_{t}}{\partial P_{a}}}{\frac{\partial I_{t}}{\partial P_{t}} } \right)^{2}   4k_{b}T_{to}^{2}G_{ta} {\mathcal{F}}(T_{to},T_{ao},\mbox{ballistic})\\
                &\sim \left( 1- \frac{G_{ta,a}}{G_{ta,a}+G_{ab}} \frac{1}{1+j \omega/\omega_{ta}}\right)^{2} 4k_{b}T_{to}^{2}G_{ta} {\mathcal{F}}\end{split}
\label{eq:Spt-Gta}$$ The insensitivity to this noise below $\omega_{ta}$ is a direct ramification of energy conservation and is a general feature of all “massless” internal thermal conductances. Of course, for the CRESST designs, this 