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Importance sampling, Fokker-Planck and Langevin equations

Consider, for instance, a simple system that has only two energy levels \epsilon_0 = 0 and \epsilon_1 = \Delta E .

For a system governed by the Boltzmann distribution we find (the partition function has been taken out)

W(0\rightarrow 1)\exp{-(\epsilon_0/kT)} = W(1\rightarrow 0)\exp{-(\epsilon_1/kT)}.

We get then

\frac{W(1\rightarrow 0)}{W(0 \rightarrow 1)}=\exp{-(\Delta E/kT)},

which goes to zero when T tends to zero.