Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

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

  • 51 Accesses

  • 2 Citations

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.

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

References

  1. 1.

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

  2. 2.

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

  3. 3.

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

  4. 4.

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

  5. 5.

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

  6. 6.

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

  7. 7.

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

  8. 8.

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

  9. 9.

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

  10. 10.

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

  11. 11.

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

  12. 12.

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

  13. 13.

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

  14. 14.

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

  15. 15.

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

  16. 16.

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

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

Key words

  • Stochastic chemical processes
  • master equation
  • exact stationary solution
  • WKB approximation