value.

The final equality arises from the fact that because the summation over the probabilities yields one, a constant function. Since this has to hold for any probability (and in particular for any probability of the form for some k) we get Using this we can write the diagonal elements as

The master equation exhibits detailed balance if each of the terms of the summation disappears separately at equilibrium--i.e. if, for all states k and l having equilibrium probabilities and ,

These

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