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On the stochastic theory of a bistable chemical reaction

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  • Borgis, D.
  • Moreau, M.

Abstract

The stochastic kinetics of a bistable chemical reaction is studied in the birth and death formalism. An elementary perturbation technique allows to estimate the first two nontrivial eigenvalues μ1 and μ2 of the evolution matrix and the corresponding engenvectors. This shows that once a quasitationary state is established in a time of order т2=∣μ2∣-1, the final evolution only changes the probability weight of each stable state, with the relaxation time т2=∣μ1∣-1⪢т2 (Kramer's time). More accurate estimation of μ2 and μ1 are proposed and compared with exact numerical results.

Suggested Citation

  • Borgis, D. & Moreau, M., 1984. "On the stochastic theory of a bistable chemical reaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(1), pages 109-130.
    • Handle: RePEc:eee:phsmap:v:123:y:1984:i:1:p:109-130
    DOI: 10.1016/0378-4371(84)90106-7
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    References listed on IDEAS

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    1. Caroli, B. & Caroli, C. & Roulet, B., 1980. "Growth of fluctuations from a marginal equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 101(2), pages 581-587.
    2. Malek-Mansour, M. & Brenig, L. & Horsthemke, W., 1977. "A stochastic approach to the kinetic theory of gases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 88(3), pages 407-424.
    3. Van den Broeck, C. & Houard, J. & Malek Mansour, M., 1980. "Chapman-Enskog development of the multivariate master equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 101(1), pages 167-184.
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