Realization of the open-boundary totally asymmetric simple exclusion process on a ring

We propose a misanthrope process, defined on a ring, which realizes the totally asymmetric simple exclusion process with open boundaries. In the misanthrope process, particles have no exclusion interactions in contrast to those in the simple exclusion process, while the hop rates depend on both numbers of particles at departure and arrival sites. Arranging the hop rates, we can recover the simple exclusion property and also make a condensate, which grows at an arbitrary single site, behave as an external reservoir providing and absorbing particles. It is known that, under some condition, the misanthrope process has an exact solution for its steady-state probability. We exploit this fact to see in an analytical way that the model proposed is exactly what we expected.