Thermal activation
= Thermal activation
<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 $r(T)=r_0\exp[-\Delta E/(k_BT)]$, an <Arrhenius equation>. The barrier $\Delta E$ controls the strong <temperature> dependence, while the prefactor $r_0$ depends on dynamics near the initial state and transition region. Plotting $\log r$ against $1/T$ tests the exponential model: a constant prefactor gives slope $-\Delta E/k_B$. 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.