$\tau\simeq 5.8$ for the same parameters as used in Fig. \[nonint\_fig\], in remarkable agreement with the simulations. However, the real threshold directly obtained by the simulation is smaller (inset of Fig. \[nonint\_fig\]). This seems not surprising considering the approximations introduced when deriving Eq. (\[T\_estimate\]). We generally adopt the practice of using $f_c$ as a single fitting parameter to study the functional dependence of the lifetime, e.g., as a function of $L$ or $T$. An example of the temperature dependence of $\tau$ in the non-interacting case is shown in Fig. \[nonint\_T\] and is also well described by Eq. .

More importantly, Eq. (\[T\_estimate\]) allows one to describe the asymptotic dependence of the lifetime on $L$. For the non-interacting case, $\tau$ is independent of the system size, consistent with previous findings [@Alicki2009; @Nussinov2008; @Hamma2009; @Bravyi2009; @Kay2008]. This fact is confirmed by our simulations, as shown in Fig. \[nonint\_fig\], where $\langle Z_{\rm ec} \rangle$ clearly approaches a step-function with increasing $L$. We also see that the bare expectation value $\langle Z \rangle $ decays even faster with larger $L$. Indeed, at sufficiently short times $t \ll 1/\max\{
\gamma(0),4\gamma(-2J)\}$, when anyon pairs have not yet diffused apart from each other (the ‘nonsplit-pair’ regime, indicated 