Exact steady states and fragmentation-induced relaxation in the no-passing asymmetric simple exclusion process

We introduce a multispecies generalization of the asymmetric simple exclusion process with a "no-passing" constraint, forbidding overtaking, on a one-dimensional reflecting (closed) chain without particle reservoirs. This no-passing rule fragments the Hilbert space into an exponential number of disjoint sectors labeled by the particle species sequence, leading to relaxation dynamics that depend sensitively on the initial ordering. We construct exact matrix-product steady states in every particle species sequence sector and derive closed-form expressions for the particle-number distribution and two-point particle correlation functions. In the two-species case, we identify a parameter regime where some sectors have finite relaxation times while others exhibit metastable relaxation dynamics, revealing the coexistence of fast and slow dynamics and strong dependence on the particle species sequence sector. Our results uncover a novel mechanism for nonequilibrium metastability arising from Hilbert space fragmentation in exclusion processes.