the investigation is usually simplified by performing a continuum limit. Since crucial properties, like the bottleneck lengths in a disordered system, might depend on the system size we have to specify this limit more carefully. We define a *weak continuum limit* where terms of ${\mathcal O}(1/L)$ are neglected while terms of ${\mathcal O}(1/\ln L)$ are kept, and a *strong continuum limit* where we even neglect terms of ${\mathcal O}(1/\ln L)$. In the following we restrict ourselves to systems where the local creation and annihilation rates $\omega_a$ and $\omega_d$ are rescaled with the system size, while the global rates $\Omega_a:=\omega_a \, L$ and $\Omega_d:=\omega_d \, L$ are kept constant. Hence $\Omega_a$ and $\Omega_d$ are system parameters while $\omega_a$ and $\omega_d$ are adjusted to the system size. In particular in the (weak and strong) continuum limit, the local rates vanish: $\omega_a,\omega_d\to 0$ for $L\to\infty$.

In homogeneous regions of these systems there is a unique [ *current-density relation (CDR)*]{} $J(\rho)$, usually called *fundamental diagram* in the context of traffic flow, that unambiguously gives the current for a given particle density $\rho=\langle \tau_j \rangle$ on any site [@popkov1], where $\tau_j=0,1$ is the occupation number of site $j$. The CDR of the TASEP has a 