Information potential and transition to criticality for certain two-species chemical systems

Using the general results of the stochastic theory of chemical systems, we consider a certain model of chemical reactions with two species, for which it is possible to calculate the first passage time explicitly and study the transition to criticality. Our method uses a non-standard Hamilton Jacobi theory for the master equation, introduced initially by Kubo et al. [J. Stat. Phys. 9 (1973) 51], which leads to solvable Hamiltonian systems.