We introduce a multi-species generalization of the asymmetric simple
exclusion process (ASEP) with a “no-passing” constraint, forbidding
overtaking, on a one-dimensional open chain. This no-passing rule fragments the
Hilbert space into an exponential number of disjoint sectors labeled by the
particle sequence, leading to relaxation dynamics that depend sensitively on
the initial ordering. We construct exact matrix-product steady states in every
particle 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 relax
in finite time while others exhibit metastable relaxation dynamics, revealing
the coexistence of fast and slow dynamics and strong particle sequence sector
dependence. Our results uncover a novel mechanism for non-equilibrium
metastability arising from Hilbert space fragmentation in exclusion processes.

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