The poisson representation. I. A new technique for chemical master equations

Abstract

We introduce a new technique for handling chemical master equations, based on an expansion of the probability distribution in Poisson distributions. This enables chemical master equations to be transformed into Fokker-Planck and stochastic differential equations and yields very simple descriptions of chemical equilibrium states. Certain nonequilibrium systems are investigated and the results are compared with those obtained previously. The Gaussian approximation is investigated and is found to be valid almost always, except near critical points. The stochastic differential equations derived have a few novel features, such as the possibility of pure imaginary noise terms and the possibility of higher order noise, which do not seem to have been previously studied by physicists. These features are allowable because the transform of the probability distribution is a quasiprobability, which may be negative or even complex.