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Nonconserving locally disordered exclusion process under constrained resources

Nisha Sharma1, Bipasha Pal2, Ankita Gupta3, and Arvind Kumar Gupta1,*

  • *Contact author: akgupta@iitrpr.ac.in
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Phys. Rev. E 113, 054136 – Published 22 May, 2026

DOI: https://doi.org/10.1103/6qq1-1995

Abstract

Driven by transport processes in natural and man-made systems, we examine a locally disordered totally asymmetric simple exclusion process with Langmuir kinetics in a resource-constrained environment. The disorder is in the form of a defect that may bind to or unbind from a particular site and slows down the particle movement, when present on the lattice. Using a mean-field approach, we analyze the steady-state behavior of the model by computing density profiles and constructing phase diagrams in the α–β parameter space, thereby revealing a rich quantitative and qualitative phase structure. The impact of finite resources and Langmuir kinetics on the stationary properties of the system is analyzed by varying the filling factor and binding constant. Upon varying the filling factor, the results uncover several critical values where the phase diagram changes qualitatively and the resulting phase complexity varies nonmonotonically. As the binding constant is increased from small values, the phase structure evolves from a limited set of phases to maximal diversity at moderate values, before settling into a simplified regime at large values. An obstruction factor is introduced to capture the combined effects of defect density and the slowdown rate in order to incorporate the role of the dynamic defect. Owing to this combined effect, increasing the obstruction factor simplifies the phase diagram, suppressing Meissner-type phases and promoting high density and shock regimes. The mean-field predictions are verified through Monte Carlo simulations implemented via Gillespie algorithm.

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References (55)

  1. J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999), pp. 1–11.
  2. J. Quastel, Introduction to KPZ, Current Developments in Mathematics (International Press, Somerville, MA, 2012), pp. 125–194.
  3. C. T. MacDonald, J. H. Gibbs, and A. C. Pipkin, Kinetics of biopolymerization on nucleic acid templates, Biopolymers 6, 1 (1968).
  4. A. Gupta, B. Pal, A. Jindal, N. Bhatia, and A. K. Gupta, Modelling of transport processes: Theory and simulations, MethodsX 10, 101966 (2023).
  5. C. T. MacDonald and J. H. Gibbs, Concerning the kinetics of polypeptide synthesis on polyribosomes, Biopolymers 7, 707 (1969).
  6. G. Schütz and E. Domany, Phase transitions in an exactly soluble one-dimensional exclusion process, J. Stat. Phys. 72, 277 (1993).
  7. B. Derrida, E. Domany, and D. Mukamel, An exact solution of a one-dimensional asymmetric exclusion model with open boundaries, J. Stat. Phys. 69, 667 (1992).
  8. A. B. Kolomeisky, G. M. Schütz, E. B. Kolomeisky, and J. P. Straley, Phase diagram of one-dimensional driven lattice gases with open boundaries, J. Phys. A: Math. Gen. 31, 6911 (1998).
  9. R. Lipowsky, S. Klumpp, and T. M. Nieuwenhuizen, Random walks of cytoskeletal motors in open and closed compartments, Phys. Rev. Lett. 87, 108101 (2001).
  10. A. Parmeggiani, T. Franosch, and E. Frey, Phase coexistence in driven one-dimensional transport, Phys. Rev. Lett. 90, 086601 (2003).
  11. S. Klumpp and R. Lipowsky, Active diffusion of motor particles, Phys. Rev. Lett. 95, 268102 (2005).
  12. D. Chowdhury, L. Santen, and A. Schadschneider, Statistical physics of vehicular traffic and some related systems, Phys. Rep. 329, 199 (2000).
  13. A. Schadschneider, Traffic flow: A statistical physics point of view, Physica A 313, 153 (2002).
  14. B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier, Exact solution of a 1D asymmetric exclusion model using a matrix formulation, J. Phys. A: Math. Gen. 26, 1493 (1993).
  15. A. K. Pandey, A. Gupta, and A. K. Gupta, Multilane bidirectional traffic in a strongly coupled exclusion model with constraint resources, Phys. Rev. E 111, 044131 (2025).
  16. M. R. Evans, R. Juhász, and L. Santen, Shock formation in an exclusion process with creation and annihilation, Phys. Rev. E 68, 026117 (2003).
  17. A. K. Verma and A. K. Gupta, Limited resources in multi-lane stochastic transport system, J. Phys. Commun. 2, 045020 (2018).
  18. A. Parmeggiani, T. Franosch, and E. Frey, Totally asymmetric simple exclusion process with Langmuir kinetics, Phys. Rev. E 70, 046101 (2004).
  19. B. Waclaw, J. Cholewa-Waclaw, and P. Greulich, Totally asymmetric exclusion process with site-wise dynamic disorder, J. Phys. A: Math. Theor. 52, 065002 (2019).
  20. L. J. Cook, R. K. P. Zia, and B. Schmittmann, Competition between multiple totally asymmetric simple exclusion processes for a finite pool of resources, Phys. Rev. E 80, 031142 (2009).
  21. A. Gupta and A. K. Gupta, Exclusion processes on a roundabout traffic model with constrained resources, Phys. Rev. E 108, 064116 (2023).
  22. C. A. Brackley, M. C. Romano, and M. Thiel, Slow sites in an exclusion process with limited resources, Phys. Rev. E 82, 051920 (2010).
  23. A. K. Pandey and A. K. Gupta, Coupled dynamics of resource competition and constrained entrances in a multi-lane bidirectional exclusion process, SciPost Phys. Core 8, 089 (2025).
  24. B. Pal and A. K. Gupta, Reservoir crowding in a resource-constrained exclusion process with a dynamic defect, Phys. Rev. E 106, 044130 (2022).
  25. C. A. Brackley, L. Ciandrini, and M. C. Romano, Multiple phase transitions in a system of exclusion processes with limited reservoirs of particles and fuel carriers, J. Stat. Mech. (2012) P03002.
  26. A. Jindal and A. K. Gupta, Exclusion process on two intersecting lanes with constrained resources: Symmetry breaking and shock dynamics, Phys. Rev. E 104, 014138 (2021).
  27. L. J. Cook and R. K. P. Zia, Feedback and fluctuations in a totally asymmetric simple exclusion process with finite resources, J. Stat. Mech. (2009) P02012.
  28. A. Jain, M. Margaliot, and A. K. Gupta, Large-scale mRNA translation and the intricate effects of competition for the finite pool of ribosomes, J. R. Soc. Interface 19, 20220033 (2022).
  29. A. Gupta and A. K. Gupta, Particle creation and annihilation in an exclusion process on networks, J. Phys. A: Math. Theor. 55, 105001 (2022).
  30. S. Tamizhazhagan and A. K. Verma, Biased dynamics of Langmuir kinetics and coupling on exclusion process, J. Stat. Phys. 191, 15 (2024).
  31. S. Muhuri, Scale-invariant density profiles of a dynamically extending TASEP, Europhys. Lett. 101, 38001 (2013).
  32. H. Yamamoto, S. Ichiki, D. Yanagisawa, and K. Nishinari, Two-lane totally asymmetric simple exclusion process with extended Langmuir kinetics, Phys. Rev. E 105, 014128 (2022).
  33. S. Garg and I. Dhiman, Dynamic disorder in a coupled two-lane exclusion process with Langmuir kinetics, Int. J. Mod. Phys. C 33, 2250142 (2022).
  34. B. Pal and A. K. Gupta, Reservoir crowding in a totally asymmetric simple exclusion process with Langmuir kinetics, Chaos Solitons Fractals 153, 111517 (2021).
  35. A. Gupta and A. K. Gupta, Non-equilibrium processes in an unconserved network model with limited resources, Eur. Phys. J. Plus 138, 108 (2023).
  36. T. Antal and G. M. Schütz, Asymmetric exclusion process with next-nearest-neighbor interaction: Some comments on traffic flow and a nonequilibrium reentrance transition, Phys. Rev. E 62, 83 (2000).
  37. P. Greulich and A. Schadschneider, Disordered driven lattice gases with boundary reservoirs and Langmuir kinetics, Phys. Rev. E 79, 031107 (2009).
  38. S. Chandel, A. Chaudhuri, and S. Muhuri, Collective transport of weakly interacting molecular motors with Langmuir kinetics, Europhys. Lett. 110, 18002 (2015).
  39. D. Botto, A. Pelizzola, M. Pretti, and M. Zamparo, Dynamical transition in the TASEP with Langmuir kinetics: Mean-field theory, J. Phys. A: Math. Theor. 52, 045001 (2019).
  40. H. D. Vuijk, R. Rens, M. Vahabi, F. C. MacKintosh, and A. Sharma, Driven diffusive systems with mutually interactive Langmuir kinetics, Phys. Rev. E 91, 032143 (2015).
  41. B. Pal and A. K. Gupta, Non-conserving exclusion process with a dynamic obstacle, Chaos Solitons Fractals 162, 112471 (2022) .
  42. S. K. Choi and M. H. Saier, Jr., Regulation of sigL expression by the catabolite control protein CcpA involves a roadblock mechanism in Bacillus subtilis: Potential connection between carbon and nitrogen metabolism, J. Bacteriol. 187, 6856 (2005).
  43. L. Qi, S. Xiao, and X. Cui, TASEP model with a single defect coupling on-ramp, in 2021 3rd International Conference on Artificial Intelligence and Advanced Manufacture (AIAM) (IEEE, New York, 2021), Vol. 23, pp. 83–88.
  44. S. Xiao, X. Chen, and Y. Liu, Totally asymmetric simple exclusion process with a single defect site on boundaries, Int. J. Mod. Phys. B 30, 1650083 (2016).
  45. C. Lin, Y. Huang, Z. Xu, and Y. Zhang, Totally asymmetric simple exclusion process on a dynamic lattice with local inhomogeneity, Results Phys. 64, 107904 (2024).
  46. N. Bhatia and A. K. Gupta, Role of site-wise dynamic defects in a resource-constrained exclusion process, Chaos Solitons Fractals 167, 113109 (2023).
  47. A. B. Kolomeisky, Asymmetric simple exclusion model with local inhomogeneity, J. Phys. A: Math. Gen. 31, 1153 (1998).
  48. P. Pierobon, M. Mobilia, R. Kouyos, and E. Frey, Bottleneck-induced transitions in a minimal model for intracellular transport, Phys. Rev. E 74, 031906 (2006).
  49. L. B. Shaw, A. B. Kolomeisky, and K. H. Lee, Local inhomogeneity in asymmetric simple exclusion processes with extended objects, J. Phys. A: Math. Gen. 37, 2105 (2004).
  50. K. Qiu, X. Yang, W. Zhang, D. Sun, and Y. Zhao, Density profiles in the totally asymmetric exclusion processes with both local inhomogeneity and Langmuir kinetics, Physica A 373, 1 (2007).
  51. A. Jindal, A. B. Kolomeisky, and A. K. Gupta, The role of dynamic defects in transport of interacting molecular motors, J. Stat. Mech. (2020) 043206.
  52. M. Sahoo, J. Dong, and S. Klumpp, Dynamic blockage in an exclusion process, J. Phys. A: Math. Theor. 48, 015007 (2015).
  53. F. Turci, A. Parmeggiani, E. Pitard, M. C. Romano, and L. Ciandrini, Transport on a lattice with dynamical defects, Phys. Rev. E 87, 012705 (2013).
  54. G. M. Schütz, On the phase transition in the sublattice TASEP with stochastic blockage, J. Phys. A: Math. Theor. 53, 425004 (2020).
  55. L. J. Cook, J. J. Dong, and A. LaFleur, Interplay between finite resources and a local defect in an asymmetric simple exclusion process, Phys. Rev. E 88, 042127 (2013).

Outline

Information

Phys. Rev. E 113, 054136– Published 22 May, 2026
  • Received 15 January 2026
  • Revised 24 March 2026
  • Accepted 1 May 2026
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