We consider an arbitrary one-dimensional conservative particle system with finite-range interactions and finite site capacity, governed on the hydrodynamic scale by a scalar conservation law with Lipschitz-continuous flux h. A finite-size perturbation restricts the local current to some maximum value $\phi$. We show that the perturbed hydrodynamic behavior is entirely determined by $\phi$ if $\inf(h;\phi)$ is first nondecreasing and then nonincreasing, which we believe is a necessary condition.
"Blockage hydrodynamics of one-dimensional driven conservative systems." Ann. Probab. 32 (1B) 805 - 854, January 2004. https://doi.org/10.1214/aop/1079021465