Journal of Statistical Physics

, Volume 14, Issue 4, pp 307–331 | Cite as

Correlations in stochastic theories of chemical reactions

  • C. W. Gardiner
  • K. J. McNeil
  • D. F. Walls
  • I. S. Matheson


A comprehensive study of correlations in linear and nonlinear chemical reactions is presented using coupled chemical and diffusion master equations. As a consequence of including correlations in linear reactions the approach to the steady-state Poisson distribution from an initial non-Poissonian distribution is given by a power law rather than the exponential predicted by neglecting correlations. In nonlinear reactions we show that a steadystate Poisson distribution is achieved in small volumes, whereas in large volumes a non-Poissonian distribution is built up via the correlation. The spatial correlation function is calculated for two examples, one which exhibits an instability, the other which exhibits a second-order phase transition, and correlation length and correlation time are calculated and shown to become infinite as the critical point is approached. The critical exponents are found to be classical.

Key words

Diffusion theory chemical reactions fluctuations instabilities master equations phase transitions stochastic processes nonequilibrium thermodynamics 


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Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • C. W. Gardiner
    • 1
  • K. J. McNeil
    • 1
  • D. F. Walls
    • 1
  • I. S. Matheson
    • 1
  1. 1.Physics DepartmentUniversity of WaikatoHamiltonNew Zealand

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