Power series solution of the inhomogeneous exclusion process

Juraj Szavits-Nossan (1) , M. Carmen Romano (2) , Luca Ciandrini (3, 4)

1 SUPA School of Physics and Astronomy [Edinburgh]
2 Institute of Complex Systems and Mathematical Biology - University of Aberdeen
3 L2C - Laboratoire Charles Coulomb
4 DIMNP - Dynamique des interactions membranaires normales et pathologiques

We develop a power series method for the nonequilibrium steady state of the inhomogeneous one-dimensional totally asymmetric simple exclusion process (TASEP) in contact with two particle reservoirs and with site-dependent hopping rates in the bulk. The power series is performed in the entrance or exit rates governing particle exchange with the reservoirs, and the corresponding particle current is computed analytically up to the cubic term in the entry or exit rate, respectively. We also show how to compute higher-order terms using combinatorial objects known as Young tableaux. Our results address the long outstanding problem of finding the exact nonequilibrium steady state of the inhomogeneous TASEP. The findings are particularly relevant to the modelling of mRNA translation in which the rate of translation initiation, corresponding to the entrance rate in the TASEP, is typically small.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Juraj Szavits-Nossan, M. Carmen Romano, Luca Ciandrini. Power series solution of the inhomogeneous exclusion process. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2018, 97, pp.052139. ⟨10.1103/PhysRevE.97.052139⟩. ⟨hal-01737998⟩