Force-tilted activation barrier ($k(F)=k_0{e}^{F\Delta x/(k_{B}T)}$)

A constant tensile force changes a one-coordinate free-energy landscape from $G_0(x)$ to $G_0(x)-Fx$. To first order, an escape barrier decreases by $F\Delta x$, where $\Delta x$ is the saddle-to-initial-minimum displacement at zero force. An approximately fixed attempt prefactor gives the displayed rate law. Its characteristic force is $F_0=k_{B}T/\Delta x$. Large changes in saddle location or competing pathways invalidate a constant activation distance. The barrier is measured relative to the initial state; an absolute saddle energy is not enough to determine an escape rate.