Abstract
Birth-and-death type master equations for linear chemical reactions in closed and open systems are solved to discuss the properties of fluctuations. For nonlinear chemical reactions the generating functions of the probability of number fluctuation are usually second order differential equations, and a method for obtaining the moments of fluctuations is presented with applications to simple examples. The deterministic kinetic equation is valid for large systems and the second moments are the same as those of Poisson distributions in open systems treated here, while for the higher moments this is not always the case.
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