Near equilibrium the second time derivative of KL divergence equals twice the Fisher information for detailed-balance Markov processes, but this equality is violated near nonequilibrium steady states, giving a bound on entropy production rate.
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Information-Geometric Signatures of Nonconservative Driving
Near equilibrium the second time derivative of KL divergence equals twice the Fisher information for detailed-balance Markov processes, but this equality is violated near nonequilibrium steady states, giving a bound on entropy production rate.