of U$_{0}$ are inconvenient for numerical integration of the Langevin equation, as a very small time increment would be required to avoid spurious particle displacements. We therefore use U$_{0}$ = 40 k$_{B}$T ≃ 9 V$_{0}$ . To begin, we consider a single Brownian particle moving in the system. Figure 2 shows a typical evolution of the particle position over time. The graph exhibits plateaux whose size corresponds to the time a particle stays in a given well. Studies of this kind allow us to determine the mean transition time τ between neighboring wells as 6.5380(9)s. This quantity is needed in order to define the insertion and removal rates. (Recall that in the lattice TASEP these rates are defined in units of the hopping rate). If the first well is empty we insert a particle there (at the potential minimum position), at rate α/τ ; if the last well is occupied, we remove the particle at rat e β/τ . FIG. 2: Typical particle trajectory. 9 0 100 200 300 400 Time [s] 20 40 60 80 100 Position [ m] 0 10 20 30 40 50 10 20 C. Single-particle dynamics