Escape or switching at short times

In the standard Arrhenius picture [S. Arrhenius, Z. Phys. Chem., Stoechiom. Verwandtschaftsl. 4, 226 (1889); L. Néel, Ann. Geophys. (C.N.R.S.) 5, 99 (1949)] of thermal switching or escape from a metastable to a stable state, the escape probability per unit time P(s)(t) decreases monotonically with time t as P(s)(t) approximately e(-t/tau(D)), where the decay time tau(D) = tau0e(U/k(B)T), with U the energy barrier, k(B)T the thermal energy, and tau0 the time between escape attempts. Here, we extend the Arrhenius picture to shorter times by deriving general conditions under which P(s)(t) is peaked rather than monotonic, and showing that in the simplest scenario the peak time tau(P) diverges with tau(D) as ln(tau(D)).