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 interaction 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 moreover have condensation if the number of particles exceeds that of sites. One condensate grows at an arbitrary single site and then behaves as an external reservoir providing and absorbing particles. It is known that, under some condition, the misanthrope process has an exact solution for the steady-state probability distribution. We exploit this to investigate the present model in an analytical manner.