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On the stationary distribution of a stochastic chemical process without detailed balance

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Abstract

An exact expression of the stationary distribution is found for a particular chemical model without detailed balance. An analytical approximation of this solution is obtained for small values of the concentration. It is shown that the WKB continuous approximation of the distribution is valid for all values of the concentration.

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References

  1. D. Mc. Quarrie,Stochastic Approach to Chemical Kinetics, Suppl. Rev. Series in Appl. Prob. (Methuen, London, 1967).

    Google Scholar 

  2. H. Haken,Rev. Mod. Phys. 47:67 (1975).

    Google Scholar 

  3. G. Nicolis and I. Prigogine,Self Organisation in Non Equilibrium System (Wiley, New York, 1977).

    Google Scholar 

  4. I. Oppenheim, K. E. Shuler, and G. H. Weiss,Stochastic Processes in Chemical Physics: The Master Equation (MIT Press, Cambridge, Massachusetts, 1977).

    Google Scholar 

  5. I. Oppenheim, K. E. Shuler, and G. H. Weiss,Physica (Utrecht) 88A:191 (1977).

    Google Scholar 

  6. K. Matsuo, K. Lindenberg, and K. E. Shuler,J. Stat. Phys. 19:65 (1978).

    Google Scholar 

  7. T. G. Kurtz,J. Chem. Phys. 57(7):2976 (1972).

    Google Scholar 

  8. R. Kubo, K. Matsuo, and K. Kitahara,J. Stat. Phys. 9:51 (1973).

    Google Scholar 

  9. W. Horsthemke and L. Brenig,Z. Phys. B27:341 (1977).

    Google Scholar 

  10. H. Lemarchand, Asymptotic solutions of the master equation near nonequilibrium transition: The stationary solutions,Physica (Utrecht),101A:518 (1980).

    Google Scholar 

  11. R. Görtz,J. Phys. A 9:1089 (1976).

    Google Scholar 

  12. R. Görtz and D. F. Walls,Z. Phys. B25:191 (1976).

    Google Scholar 

  13. M. Malek-Mansour and G. Nicolis,J. Stat. Phys. 13(3):197 (1975).

    Google Scholar 

  14. M. Moreau,Physica (Utrecht) 102A:389 (1980).

    Google Scholar 

  15. J. Keiser,J. Chem. Phys. 63(1):398 (1975);J. Chem. Phys. 63(11):5037 (1975).

    Google Scholar 

  16. J. Keiser,J. Chem. Phys. 67(4): 1473 (1977).

    Google Scholar 

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Dambrine, S., Moreau, M. On the stationary distribution of a stochastic chemical process without detailed balance. J Stat Phys 26, 137–148 (1981). https://doi.org/10.1007/BF01106790

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  • DOI: https://doi.org/10.1007/BF01106790

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