Consider an electron that can transition between two levels by emitting or absorbing a photon; and recall that we have argued that the stimulated transitions should be microscopically reversible. This is an example of a general principle introduced by Boltzmann called detailed balance. In the context of classical physics, it is usually considered in the context of the time reversibility of the underlying physical equations. For example, if two molecules collide elastically and exchange energy, the time-reversed process happens with the same probability per unit time when the colliding particles are in the time-reversed initial states. However, this does not necessarily imply that the probability of a single molecule changing its velocity from v to v' is the same as that of the reverse change. (A high-energy molecule is more likely to lose energy when one averages over all collisions.)

An important simplification happens when the probability of a change in y is equal to the probability of the opposite change. An example might be a light particle colliding with a heavy particle for which the recoil can be ignored. Under this more restrictive condition, we can write that

Show that the Fokker-Planck equation then simplifies (under the usual assumptions) to a standard diffusion equation:

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P(y', Δty) = P(ν, Δty').