TASEP and integrable many-body system

We consider a new duality between the discrete-time inhomogeneous multispecies TASEP model on the circle and the quantum Goldfish model from the Ruijsenaars-Schneider family. We present the precise map of the inhomogeneous multispecies TASEP system and 5-vertex model, which are the limiting cases of 6-vertex model, to the trigonometric and rational Goldfish models respectively, where the TASEP local jump rates get identified as the coordinates in the Goldfish model. This is a joint work with A. Gorsky and A. Zotov.