Abstract
We introduce the multispecies totally asymmetric simple exclusion process (mTASEP) with long-range swap, a new interacting particle system combining the backward-push rule with the forward-jump rule.Although governed by local dynamics, the model induces effective longrange particle exchanges.We establish its integrability by proving two-particle reducibility and showing that the associated scattering matrix satisfies the Yang-Baxter equation.In addition, we derive explicit contour integral formulas for transition probabilities.These results position the long-range swap model as a novel exactly solvable multispecies process, characterized by distinctive algebraic features and opening new directions for further study in integrable probability and statistical mechanics.