within the transition that is sensitive to temperature fluctuations [@blas_overview].

Although a computational simulation of phase separation within the CRESST geometry is beyond the scope of this paper (and of dubious value without a very careful matching to experimental data since the dynamics depend on the resistivity of the entire transition, rather than at a single operation point), we can qualitatively discuss the ramifications.

Most importantly, a phase separated TES has significantly suppressed thermal sensitivity when biased. To see this, we note that in the limit of $\alpha =
\frac{T}{\rho}\frac{\partial \rho}{\partial T} \rightarrow \infty$ (i.e. the super conducting transition becoming infinitely sharp and infinitely sensitive to temperature variation), the DC response of the TES can be modeled analytically by tracking the fractional location of the superconducting/normal transition in the TES, $x$, as a function of $V_{b}$ and $T_{b}$ [@circleTES]. For the pertinent case where the electron-phonon coupling along the TES is negligible compared to power flow through the connection to the bath at one end of the TES, the thermal power flowing across the superconducting portion of the TES is constant and can be matched to the joule heating in the normal portion of the TES: $${\left(\frac{V_{b}}{R_{l} + R_{n}x}\right)}^{2} R_{n} 