Dj. Bicout et A. Szabo, FIRST PASSAGE TIMES, CORRELATION-FUNCTIONS, AND REACTION-RATES, The Journal of chemical physics, 106(24), 1997, pp. 10292-10298
The mean lifetime of a particle in the presence of an absorbing bounda
ry is the mean first passage time to the boundary. For diffusive dynam
ics on a one dimensional potential, we establish an exact relation bet
ween the mean first passage time to x=a averaged over a (pseudo) equil
ibrium distribution in the region a less than or equal to x<infinity,
and the time integral of certain equilibrium correlation functions det
ermined by dynamics on the entire (-infinity<x<infinity) surface in th
e 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 b
arrier crossing obtained using mean first passage times and obtained f
rom the time integral of the normalized number correlation function, a
re identical for an arbitrary choice of the dividing surface. (C) 1997
American Institute of Physics.