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We propose the entropy of random Markov trajectories originating andterminating at a state as a measure of the stability of a state of a Markovprocess. These entropies can be computed in terms of the entropy rates andstationary distributions of Markov processes. We apply this definition ofstability to local maxima and minima of the stationary distribution of theMoran process with mutation and show that variations in population size,mutation rate, and strength of selection all affect the stability of thestationary extrema.

Entropic Equilibria Selection of Stationary Extrema in Finite Populations