2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164011We consider the totally asymmetric exclusion process on a ring in discrete time with the backward-ordered sequential update and particle-dependent hopping probabilities. Using a combinatorial treatment of the Bethe ansatz, we derive the determinant expression for the non-stationary probability of transitions between particle configurations. In the continuous-time limit, we find a generalization of the recent result, obtained by A. Rákos and G.M. Schütz for infinite lattice, to the case of ring geometry.4 pages, RevTeX4, 2 EPS figuresStatistical MechanicsSoft Condensed Mattertext