Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S12 / 2 / 3 / Solution

The stationary occupation ratio is $p_1/p_2=2$. Balance of the two probability currents gives $p_1{k}_{12}=p_2{k}_{21}$, and Boltzmann occupation of the trapped macrostates gives $p_2/p_1=e^{-(G_2-G_1)/(k_{B}T)}$. ThereforeThe sketch has two wells separated by 1 micrometre, with the second free-energy level higher by $k_{B}T\log 2$ and an intervening escape barrier. Free energy includes the volume of each trapped basin; equal minimum potential heights alone would not ensure equal occupations if basin shapes differed.