The minimal KL divergence rate D(P* || Q) lower-bounds the power to control a Markov chain to a desired stationary distribution, with explicit solutions for reversible chains and birth-death processes.
A representation formula for the large deviation rate function for the empirical law of a continuous time Markov chain,
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Minimum Power to Maintain a Nonequilibrium Distribution of a Markov Chain
The minimal KL divergence rate D(P* || Q) lower-bounds the power to control a Markov chain to a desired stationary distribution, with explicit solutions for reversible chains and birth-death processes.