Power series solution of the inhomogeneous exclusion process

Juraj Szavits-Nossan, M. Carmen Romano, Luca Ciandrini

Research output: Contribution to journalArticlepeer-review


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 modeling of mRNA translation in which the rate of translation initiation, corresponding to the entrance rate in the TASEP, is typically small.
Original languageEnglish
Article number052139
Number of pages13
JournalPhysical Review E
Issue number5
Publication statusPublished - 29 May 2018


  • perturbation techniques


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