Clustering in two models of interacting motors

We study a two-species bidirectional exclusion process, and a single species variant, which is motivated by the motion of organelles and vesicles along microtubules. Specifically, we are interested in the clustering of the particles and appearance of a single large cluster as the ratio \(Q\) of the translation to switching rates is varied. We find that, although for a finite system, there is a clustering phenomenon in which the probability of finding a single large cluster changes from being negligible to having finite values, the phenomenon shifts to larger \(Q\) values as the system size is increased. This suggests that the observed clustering is not a true (nonequilibrium) transition in the thermodynamic sense but rather a finite-size effect.