single maximum. Later, when we will also consider more general driven lattice gases, we will always assume that their CDR also has a single maximum. The maximum is at the point $\rho_M$ and takes the value $J_M=J(\rho_M)$. In this case for a given current $J$, two possible values for the density, the *high density value* $\rho_H(J)>\rho_M$ and the *low density value* $\rho_L(J)<\rho_M$ exist.

For these systems, the non-conservation of particles can be expressed by a source term in the equation of continuity of the stationary state [^2]: $$\label{continuity_equ}
J_j-J_{j-1}=s(\rho) \,$$ where $J_j$ is the current through the bond between sites $j$ and $j+1$. The attachment of particles is assumed to be inhibited by particles occupying sites, so we assume $s(\rho)$ to be a globally decreasing function. In fact one can construct models with attractive interactions where $s(\rho)$ is an increasing function. However, those systems might exhibit non-ergodic behaviour [@schuetz_nonergodic] that we do not consider here. Since $\omega_a,\omega_d\to 0$ in the continuum limit, we also have $s(\rho)\to 0$ in this limit. Hence locally the current is *almost constant* for large systems and the CDR is the same as in the corresponding system without LK [@popkov1; @diplom].

The time evolution per time 