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.
|Number of pages||13|
|Journal||Physical Review. E, Statistical, Nonlinear and Soft Matter Physics|
|Publication status||Published - 29 May 2018|
Bibliographical noteJ.S.N. was supported by the Leverhulme Trust Early Career Fellowship under Grant No. ECF-2016-768. M.C.R. was supported by the Biotechnology and Biological Sciences Research Council (BBSRC) Grant No. BB/N017161/1 and the Scottish Universities Life Sciences Alliance. L.C. would like to thank the CNRS for having granted him a “demi-délégation” (2017–18).
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- School of Natural & Computing Sciences, Physics - Personal Chair
- Institute for Complex Systems and Mathematical Biology (ICSMB)