Abstract
Abstract We introduce a class of multispecies exclusion processes in which each species follows its own intra-species interaction mechanism. In contrast to previously studied integrable multispecies models—such as the multispecies TASEP, where the intra-species interaction rule is identical across all species—our framework allows the intra-species rule to vary across species, while inter-species interactions obey a long-range swap rule. We prove that Bethe ansatz integrability is preserved in the binary regime, where each species follows either TASEP-type or drop-push-type dynamics, by establishing the Yang–Baxter structure of the associated scattering matrices. Furthermore, we identify nontrivial families of species compositions through a continuous interpolation between these dynamics that remain integrable, and extend the model to include bidirectional motion. These results show that Bethe ansatz integrability extends to a broad class of multispecies systems with species-dependent interaction mechanisms, providing a framework for deriving exact transition probabilities and analyzing nonequilibrium dynamics.