  We consider the one-dimensional Katz-Lebowitz-Spohn (KLS) model, which is a
two-parameter generalization of the Totally Asymmetric Simple Exclusion Process
(TASEP) with nearest neighbour interaction. Using a powerful mapping, the KLS
model can be translated into a misanthrope process. In this model, for the
repulsive case, it is possible to introduce second class particles, the number
of which is conserved. We study the distance distribution of second class
particles in this model numerically and find that for large distances it
decreases with a power -3/2. This agrees with a previous analytical result for
the TASEP where the same asymptotic behaviour was found [Derrida et al. 1993].
We also study the dynamical scaling function of the distance distribution and
find that it is universal within this family of models.
