profile is *not flat* and *stationary shocks* can occur in the bulk. For particle conserving systems these are not possible [@popkov1; @evans_pff].

2.  In the homogeneous TASEP, the current is restricted by the upper bound $J^{\rm max}_{\rm hom}=p(1-p)=0.25$ (for hopping rate $p=1$) due to the bulk exclusion. Already a single defect site with lower hopping rate $q<p$ reduces this maximum stationary current [@lebowitz1]. In [@pff_1def] it was shown that also in the TASEP/LK a single defect site $d$ restricts the current by a value $J^*_d:=J^{\rm max}_d<J^{\rm max}_{\rm hom}$ at this site, that cannot be exceeded by tuning external parameters. The quantity $J^*_d$ is exactly the local *transport capacity* defined in Sec. \[model\_sec\]. However, due to the spatially varying current, this effect is only *local* and the maximum value of the current $J^{\rm max}_i$ on sites $i$ far away from the defect can be larger than $J^*_d$. For completeness, we define $J^*_i=J^{\rm
      max}_{\rm hom}$ on non-defect sites $i$, so the transport capacity is peaked on a single site. If the current imposed by the boundary rates is larger than the transport capacity of a defect, phase separation occurs, exhibiting stationary shocks. In the inhomogeneous TASEP no stationary shocks can occur in 