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Stationary densities in a weakly nonconserving asymmetric exclusion process with finite resources

Sourav Pal* and Abhik Basu†

  • *Contact author: isourav81@gmail.com
  • †Contact author: abhik.123@gmail.com; abhik.basu@saha.ac.in
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Phys. Rev. E 114, 034121 – Published 11 September, 2026

DOI: https://doi.org/10.1103/sr5v-jwxp

Abstract

Inspired by the phenomenologies of an open totally asymmetric simple exclusion process (TASEP) with Langmuir kinetics (Lk) and finite resources that dynamically control the entry and exit rates of the TASEP lane, we study the stationary densities and phase transitions in a TASEP with Lk connected to both ends of a particle reservoir. The resulting phase diagrams in the plane of the control parameters are significantly different from those in an open TASEP with Lk. In particular, some of the phases admissible in the open TASEP with Lk model are no longer possible. Intriguingly, our model is closely related to a TASEP coupled with Lk on a ring with a point defect, but admits more phases than the latter. Phenomenological implications of our results are discussed.

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Phys. Rev. E 114, 034121– Published 11 September, 2026
  • Received 1 April 2026
  • Revised 10 August 2026
  • Accepted 20 August 2026
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