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The double well curve represents the potential of mean force for a hypothetical pair of states in equilibrium separated by a barrier. If the barrier height fluctuates the dynamics between the two states will appear non-Markovian. The model is, of course, Markovian at higher-order. If the barrier fluctuates, for example, between two states, then a 4-state potential of mean force like that on the right may be more appropriate as a description.
