Metastable lifetime for a class of chemical systems near criticality

We consider a n-dimensional autocatalytic chemical system with a finite metastable state which tends to become critical. Away from the critical situation, the relaxation time from the metastable state to the final absorbing state can be computed by using inverse of the stationary probability distribution of the system at its minimal value. It is difficult to obtain explicit results on the stationary probability distribution in general for several variables. Nevertheless, we can estimate this quantity near criticality and we show that its critical exponent is 2 under rather general conditions. This result is verified explicitly on an example, for which a direct calculation can be done.