On the lattice, the current is equal to the probability of having an occupied site with its neighbor on the right vacant, i. e., J = 〈 ξ$_{i}$ (1 − ξ$_{i}$$_{+1}$ ) 〉 , ∀ i , where ξ$_{i}$ is an indicator variable equal to one if site i is occupied and 0 if it is empty. In mean-field theory the joint probability is factored so: 〈 ξ$_{i}$ (1 − ξ$_{i}$$_{+1}$ ) 〉 = 〈 ξ$_{i}$ 〉〈 (1 − ξ$_{i}$$_{+1}$ ) 〉 , and setting 〈 ξ$_{i}$ 〉 = ρ in the bulk, we obtain J = ρ (1 − ρ ). In developing a mean-field theory for the continuous-space model, one might argue that J ≃ ρ (1 − ρ ) /τ , i. e., that the current is simply given by the transition rate 1 /τ for jumps between neighboring wells times the probability of a given well being occupied and its right neighbor empty. Due to repulsive interactions between neighboring particles, however, a particle in the well to the left can also influence the hopping rate. As a first approximation we write where P ( ξ$_{i}$$_{−}$$_{1}$, ξ$_{i}$, ξ$_{i}$$_{+1}$ ) is the joint probability for three adjacent wells, and j ( ξ$_{i}$$_{−}$$_{1}$, ξ$_{i}$, ξ$_{i}$$_{+1}$ ) is the transition rate in this configuration. Factorizing the joint probability, we have P (0 , 1 , 0) = ρ (1 − ρ ) 2 and P (1 , 1 , 0) = ρ $^{2}$(1 − ρ ). It remains to evaluate the currents j (0 , 1 , 0) and j (1 , 1 , 0). Consider first j (0 , 1 , 0), the rate to overcome the barrier between wells i and i +1, given that both i − 1 and i + 1 are empty. The mean first-passage time τ$_{ca}$ , for a particle to overcome the barrier, is readily found via analysis of the one-dimensional Fokker-Planck equation. From the standard result [28] we have where a = x$_{0}$ and c = x$_{0}$ + 2 d$_{0}$ are the positions of adjacent potential minima, with x$_{0}$ given by Eq. (13). Using the effective external potential, Eq. (11), for U ( x ) (since there are no interactions with other particles), numerical evaluation of Eq. (19) yields τ$_{ca}$ = 6 . 538 s = 1 /j (0 , 1 , 0). This value agrees to within uncertainty τ$_{ca}$ = 1 k$_{B}$T ∫ c a e U ( x $^{′}$) /k$_{B}$$^{T}$dx ′ ∫ x ′ −∞ e − U ( x $^{′′}$) /k$_{B}$$^{T}$dx $^{′′}$, (19) 20 J = P (0 , 1 , 0) j (0 , 1 , 0) + P (1 , 1 , 0) j (1 , 1 , 0) , (18)