Analytic theory of extrema. III. Results for master equations with application to unimolecular decomposition

We obtain exact expressions for the mean first passage time to reach a given state in systems described by a master equation. Our results are simple and lend themselves to direct physical interpretation and to a straightforward asymptotic analysis. An asymptotic series is obtained for the mean first passage time that is rapidly convergent in many cases and that is easy to implement. We apply our formulas to the problem of unimolecular dissociation and calculate the deviation of the dissociation rate from that obtained using statistical theories.