First passage times, correlation functions, and reaction rates

The mean lifetime of a particle in the presence of an absorbing boundary is the mean first passage time to the boundary. For diffusive dynamics on a one dimensional potential, we establish an exact relation between the mean first passage time to x=a averaged over a (pseudo) equilibrium distribution in the region a less than or equal to x<infinity, and the time integral of certain equilibrium correlation functions determined by dynamics on the entire (-infinity<x<infinity) surface in the absence of an absorbing boundary at x=a. As an application, we show that the sum of the forward and reverse rate constants for diffusive barrier crossing obtained using mean first passage times and obtained from the time integral of the normalized number correlation function, are identical for an arbitrary choice of the dividing surface. (C) 1997 American Institute of Physics.