Abstract
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.
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Gardiner, C.W., McNeil, K.J., Walls, D.F. et al. Correlations in stochastic theories of chemical reactions. J Stat Phys 14, 307–331 (1976). https://doi.org/10.1007/BF01030197
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DOI: https://doi.org/10.1007/BF01030197