Integrable Multispecies Totally Asymmetric Stochastic Interacting Particle Systems with Homogeneous Rates

We study one-dimensional stochastic particle systems with exclusion interaction—each site can be occupied by at most one particle—and homogeneous jumping rates. Earlier work of Alimohammadi and Ahmadi classified 28 Yang–Baxter integrable two-particle interaction rules for two-species models with homogeneous rates. In this work, we show that 7 of these 28 cases can be naturally extended to integrable models with an arbitrary number of species N≥2. A key novelty of our approach is the discovery of new integrable families with one or two continuous parameters that generalize these seven cases, significantly broadening the known class of multispecies integrable exclusion processes. Furthermore, for 8 of the remaining 21 cases, we propose an alternative extension scheme that also yields integrable N-species models, thereby opening new directions for constructing and classifying integrable particle systems.