Skip to main content
SpringerLink
Log in

Nonequilibrium phase transitions in a two-channel ASEP with binding energies and analytical evaluations via Kullback–Leibler divergence

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

In order to reflect new physical insights in understanding nonequilibrium phase transition mechanisms of real mesoscopic transport, a new exclusion process with horizontal and vertical binding energies is constructed. Fruitful developments of mean-field theories including developed simple, 2-lattice cluster, 4-lattice cluster and correlation mean-field theories are given. Typical order parameters are analytically solved and verified by simulation statistics. Evolution laws of phase boundaries with varied lane-changing rates, mobilities and binding energies are found via acquisitions of density profiles and phase diagrams. Fitting effects of developed analytical methods are quantitatively compared via Kullback–Leibler divergence. Findings show that developed simple mean-field theory (SMF) achieves better results in the fitting of each phase, while developed 2-lattice cluster mean-field theory (CMF) has better results in the fitting of low-density and coexistence phases. Developed 4-lattice CMF has better results in fitting low-density phase and high-density part of coexistence one, and developed correlation cluster mean-field theory (CCMF) has better results in the fitting except high-density phase. The minimum correlation element is introduced to explain differences among evaluations of analytical solutions under Kullback–Leibler divergence. The minimum correlation element size of SMF, CCMF, 2-lattice CMF and 4-lattice one is found to be 1, 1.5, 2 and 4, respectively. Intrinsic dynamics are found to have a great impact on analysis solutions, which indicate that analytical results brought by different minimum correlation elements need to be comprehensively considered to determine correlation degree, although evaluation results reveal that deviations between analytical solutions and simulation results increase with the minimum size of the related element. Effectiveness of developed theories is achieved in a more scientifically sound manner, which is helpful for evaluating rationality and effectiveness of analytical methods and critical phenomena of spatial correlations in nonequilibrium multi-body particle interaction systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Data availability

This manuscript has associated data in a data repository. [Authors’ comment: The data calculated and obtained by authors are uploaded to the repository “figshare” with the available hyperlink https://figshare.com/articles/dataset/All_source_data_of_submitted_manuscript/19153754. Citation information of authors’ data is: Wang, Yu-Qing; Li, Tian-Ze; Fang, Mo-Lin; Diao, Jian-Shu; Long, Yi; Wang, Hao-Tian; et al. (2022): All_source_data_of_submitted_manuscript. figshare. Dataset. https://doi.org/10.6084/m9.figshare.19153754.v1].

References

  1. K. Mainzer, Eur. Rev. 13(S2), 29–48 (2005)

    Article  Google Scholar 

  2. R.M. May, Nature 238(5364), 413–414 (1972)

    Article  ADS  Google Scholar 

  3. Y. Shen, B. Tian, T.Y. Zhou, Eur. Phys. J. Plus 136(5), 1–18 (2021)

    ADS  Google Scholar 

  4. H. Haken, Synergetics 1, 5–30 (2020)

    Google Scholar 

  5. M. Wang, B. Tian, S.H. Liu et al., Eur. Phys. J. Plus 136(6), 1–13 (2021)

    Article  Google Scholar 

  6. R.A. Blythe et al., Phys. Rev. Lett. 89(8), 080601 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  7. F.Y. Liu, Y.T. Gao, X. Yu et al., Eur. Phys. J. Plus. 136(6), 1–14 (2021)

    Article  ADS  Google Scholar 

  8. X. Lü et al., Eur. Phys. J. B 72(2), 233–239 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  9. T. Hanney, M.R. Evans, J. Stat. Phys. 111(5), 1377–1390 (2003)

    Article  Google Scholar 

  10. S.J. Chen, X. Lü, M.G. Li et al., Phys. Scrip. 96(9), 095201 (2021)

    Article  ADS  Google Scholar 

  11. D. Chowdhury et al., Phys. Rep. 329(4–6), 199–329 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  12. K. Mallick, Phys. A 418, 17–48 (2015)

    Article  Google Scholar 

  13. S.S. Poghosyan et al., J. Stat. Mech. 2010(04), P04022 (2010)

    Article  Google Scholar 

  14. R.K.P. Zia et al., J. Stat. Mech. 2007(07), P07012 (2007)

    Article  Google Scholar 

  15. L. Davis, T. Gedeon, J. Gedeon et al., J. Math. Bio. 68(3), 667–700 (2014)

    Article  Google Scholar 

  16. D.E. Andreev et al., Elife 7, e32563 (2018)

    Article  Google Scholar 

  17. P. Chvosta et al., New J. Phys. 7(1), 190 (2005)

    Article  ADS  Google Scholar 

  18. S. Muhuri, Euro. Lett. 101(3), 38001 (2013)

    Article  ADS  Google Scholar 

  19. D.M. Miedema et al., Phys. Rev. X 7(4), 041037 (2017)

    Google Scholar 

  20. O. Golinelli, K. Mallick, J. Phys. A 39(41), 12679 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  21. F. Paul, H. Wu, M. Vossel et al., J. Chem. Phys. 150(16), 164120 (2019)

    Article  ADS  Google Scholar 

  22. D. Botto et al., J. Phys. A 52(4), 045001 (2018)

    Article  ADS  Google Scholar 

  23. D. Botto et al., J. Phys. A 53(34), 345001 (2020)

    Article  MathSciNet  Google Scholar 

  24. A. Jindal, A.K. Gupta, Chaos Soliton. Fract. 152, 111354 (2021)

    Article  Google Scholar 

  25. Dhiman I., Gupta A.K., Inter. J. Mod. Phys. C, 2018; 29(04): 1850037.

  26. P. Greulich, L. Ciandrini, R.J. Allen et al., Phys. Rev. E 85(1), 011142 (2012)

    Article  ADS  Google Scholar 

  27. F. Turci, A. Parmeggiani, E. Pitard et al., Phys. Rev. E 87(1), 012705 (2013)

    Article  ADS  Google Scholar 

  28. P. Hrabák, J. Traff. Transp. Eng. 7(1), 30–41 (2020)

    Google Scholar 

  29. E. Aas, A. Ayyer, S. Linusson et al., J. Phys. A 52(35), 355001 (2019)

    Article  MathSciNet  Google Scholar 

  30. J. Szavits-Nossan et al., J. Stat. Mech. 2009(12), P12019 (2009)

    Article  Google Scholar 

  31. A.K. Gupta, J. Stat. Phys. 162(6), 1571–1586 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  32. A. Pelizzola, M. Pretti, Eur. Phys. J. B 90(10), 1–8 (2017)

    Article  Google Scholar 

  33. B. Tian et al., Eur. Lett. 128(4), 40005 (2020)

    Article  Google Scholar 

  34. S. Mukherji, Phys. Rev. E 97(3), 032130 (2018)

    Article  ADS  Google Scholar 

  35. N. Sharma et al., J. Stat. Mech. 2017(4), 043211 (2017)

    Article  Google Scholar 

  36. N.A. Slavnov, Teoret. Mat. Fiz. 79(2), 232–240 (1989)

    MathSciNet  Google Scholar 

  37. Möckel M., Real-time evolution of quenched quantum systems, LMU, 2009.

  38. N.M. Bogoliubov, Theor. Math. Phys. 175(3), 755–762 (2013)

    Article  Google Scholar 

  39. B. Tian et al., Phys. A 541, 123542 (2020)

    Article  Google Scholar 

  40. E. Frey, K. Kroy, Ann. Phys. 14(1–3), 20–50 (2005)

    Google Scholar 

  41. Kavanagh K., Dooley S., Slingerland J.K. et al., New J. Phys., 2022.

  42. J. Merikoski, Phys. Rev. E 88(6), 062137 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  43. M. Gorissen et al., J. Phys. A 44(11), 115005 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  44. M. Gorissen et al., Phys. Rev. E 79(2), 020101 (2009)

    Article  ADS  Google Scholar 

  45. J.J. Dong et al., J. Phys. A 42(1), 015002 (2008)

    Article  ADS  Google Scholar 

  46. S. Dorosz et al., Phys. Rev. E 81(4), 042101 (2010)

    Article  ADS  Google Scholar 

  47. T. Midha et al., Phys. Rev. E 98(4), 042119 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  48. A. Jindal et al., J. Phys. A 53(23), 235001 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  49. Midha T., Gupta A.K., Bio. Commun. Supp., 2018; 5(1).

  50. V. Lecomte et al., J. Stat. Phys. 127(1), 51–106 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  51. R.I. Mukhamadiarov, U.C. Täuber, Phys. Rev. E 100(6), 062122 (2019)

    Article  ADS  Google Scholar 

  52. D. Chowdhury et al., Phys. Rev. E 65(4), 046126 (2002)

    Article  ADS  Google Scholar 

  53. D. Orr, L. Petrov, Adv. Math. 317, 473–525 (2017)

    Article  MathSciNet  Google Scholar 

  54. R.K.P. Zia et al., J. Stat. Phys. 144(2), 405–428 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  55. Gorsky A., Vasilyev M., Zotov A., arXiv, 2021; 2109.05562.

  56. A. Lazarescu, J. Phys. A 46(14), 145003 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  57. F.H. Jafarpour et al., J. Phys. A 38(21), 4579 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  58. J.B. Martin, Elect. J. Prob. 25, 1–41 (2020)

    Google Scholar 

  59. A. Lazarescu, V. Pasquier, J. Phys. A 47(29), 295202 (2014)

    Article  MathSciNet  Google Scholar 

  60. V. Belitsky et al., J. Phys. A 46(29), 295004 (2013)

    Article  MathSciNet  Google Scholar 

  61. B. Derrida et al., J. Stat. Phys. 94(1), 1–30 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  62. P. Helms et al., Phys. Rev. E 100(2), 022101 (2019)

    Article  ADS  Google Scholar 

  63. V. Popkov et al., J. Stat. Phys. 142(3), 627–639 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  64. S. Das, W. Zhu, Elect. J. Probab. 27, 1–34 (2022)

    Google Scholar 

  65. B. Derrida et al., Phys. Rev. Lett. 89(3), 030601 (2002)

    Article  ADS  Google Scholar 

  66. X.Y. Gao et al., Appl. Math. Lett. 120, 107161 (2021)

    Article  Google Scholar 

  67. X.Y. Gao et al., Commun. Theor. Phys. 72(9), 095002 (2020)

    Article  ADS  Google Scholar 

  68. X.Y. Gao et al., Chaos Soliton. Fracta. 150, 111066 (2021)

    Article  Google Scholar 

  69. X.Y. Gao et al., Eur. Phys. J. Plus 136(8), 1–9 (2021)

    Article  ADS  Google Scholar 

  70. M. Wang et al., Appl. Math. Lett. 119, 106936 (2021)

    Article  Google Scholar 

  71. Y. Shen, Appl. Math. Lett. 122, 107301 (2021)

    Article  Google Scholar 

  72. X.T. Gao et al., Chaos Soliton. Fracta. 151, 111222 (2021)

    Article  Google Scholar 

  73. D.Y. Yang et al., Chaos Soliton. Fracta. 150, 110487 (2021)

    Article  Google Scholar 

  74. M.Z. Yin et al., Nonlinear Dyn. 106, 1347 (2021)

    Article  Google Scholar 

  75. S.J. Chen et al., Phys. Scrip. 96, 095201 (2021)

    Article  ADS  Google Scholar 

  76. X. Lü, Nonlinear Dyn. 106, 1491 (2021)

    Article  Google Scholar 

  77. X.J. He et al., Math. Comp. Sim. 197, 327 (2022)

    Article  Google Scholar 

  78. S.J. Chen et al., Commun. Nonlinear Sci. Num. Sim. 109, 106103 (2022)

    Article  Google Scholar 

  79. X. Lü, Commun. Nonlinear Sci. Num. Sim. 103, 105939 (2021)

    Article  Google Scholar 

  80. L.A. Kumaraswamidhas et al., Measurement 174, 108948 (2021)

    Article  Google Scholar 

  81. J. Le et al., Ener. Rep. 7, 5203–5213 (2021)

    Article  Google Scholar 

  82. X. Yang et al., Adv. Neur. Infor. Process. Syst. 34, 1 (2021)

    Google Scholar 

  83. Y. Cao et al., Chemo. Intel. Lab. Syst. 210, 104230 (2021)

    Article  Google Scholar 

  84. H. Hess, V. Vogel, Rev. Mole. Bio. 82(1), 67–85 (2001)

    Article  Google Scholar 

  85. M. Vershinin et al., PNAS 104(1), 87–92 (2007)

    Article  ADS  Google Scholar 

  86. T. Van Erven, P. Harremos, IEEE Trans. Inform. Theo. 60(7), 3797–3820 (2014)

    Article  Google Scholar 

Download references

Acknowledgment

This research is supported by projects below: National Natural Science Foundation of China (Grant No. 11705042), Collaborative Education Project of Industry University Cooperation of Ministry of Education (Grant No. 202101073009), Quality Engineering Project of Anhui Provincial Department of Education (Grant No. 2020kfkc400), Curriculum Research Project of Hefei University of Technology (Grant No. 11020–03,392,021,003), Publishing Fund of Hefei University of Technology (Grant No. HGDCBJJ2020039), the China Postdoctoral Science Foundation (Grant Nos. 2018T110040, 2016M590041) and the Fundamental Research Funds for the Central Universities (Grant No. JZ2018HGTB0238). Prof. Yu-Qing Wang, Dr. Tian-Ze Li and Dr. Mo-Lin Fang contributed equally.

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Hefei University of Technology, Hefei, 230009, China

    Yu-Qing Wang

  2. Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China

    Tian-Ze Li, Mo-Lin Fang, Jian-Shu Diao, Yi Long, Yun-Zhi Wang, Hao-Song Sun, Ming-Cheng Zhao & Wei-Chen Zhang

  3. School of Life Sciences, University of Science and Technology of China, Hefei, 230027, China

    Hao-Tian Wang

  4. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Chu-Zhao Xu & Zhao-Chen Wang

Authors
  1. Yu-Qing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tian-Ze Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mo-Lin Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jian-Shu Diao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yi Long
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hao-Tian Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yun-Zhi Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Hao-Song Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Chu-Zhao Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Ming-Cheng Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Zhao-Chen Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Wei-Chen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu-Qing Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, YQ., Li, TZ., Fang, ML. et al. Nonequilibrium phase transitions in a two-channel ASEP with binding energies and analytical evaluations via Kullback–Leibler divergence. Eur. Phys. J. Plus 137, 505 (2022). https://doi.org/10.1140/epjp/s13360-022-02708-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-02708-5

Search

Navigation