Thermal activation is barrier crossing enabled by thermal fluctuations. A system can remain for a long time near a local minimum of an energy landscape, then receive a fluctuation large enough to cross an energy barrier. Its most probable state and its waiting time for escape are therefore different questions.
In a simple high-barrier regime, the escape rate is approximated by , an Arrhenius equation. The barrier controls the strong temperature dependence, while the prefactor depends on dynamics near the initial state and transition region. Plotting against tests the exponential model: a constant prefactor gives slope . Interpreting a slope still requires care if several escape paths compete or the prefactor varies with temperature. A large barrier can delay approach to thermal equilibrium even when the final equilibrium state is known.
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