Stochastic theory of bistable reactions

The motivation for studying bistable reaction systems came from two different directions. First, a model of a Brownian particle moving in a 

The estimation of relaxation times from the Fokker-Planck equations was discussed by Matsuno et al. (1978). A Fokker-Planck equation can be written as 

In the physical literature, adopting the Landau-Ginzburg picture, U is often referred to as the free energy . In the chemical context it is better to use the term free-energy-like . The stationary states of the system occur at the extrema of f/(x). Metastable states can be identified with local minima. The relaxation time of the process leading from metastable to stable state is estimated as 

This formula shows not only the exponential dependence of the relaxation time on the system size, but also the effect of the height of the potential barrier (f/(xj - U xJ). 

Estimation of relaxation times from the master equation using spectral analysis of the coefficients matrix was used by Dambrine Moreau (1981a, b) for a chemical system having a finite state-space. The reaction 

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