Simple relations between mean passage times and Kramers' stationary rate

The classical problem of the escape time of a metastable potential well in a thermal environment is generally studied by various quantities like Kramers' stationary escape rate, mean first passage time, nonlinear relaxation time, or mean last passage time. In addition, numerical simulations lead to the definition of other quantities as the long-time limit escape rate and the transient time. In this paper, we propose some simple analytical relations between all these quantities. In particular, we point out the hypothesis used to evaluate these various times in order to clarify their comparison and applicability, and show how average times include the transient time and the long-time limit of the escape rate.