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Transition records of stationary Markov chains

Jan Naudts·Erik Van der Straeten
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Abstract

In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary Markov chain is linear in the number of steps. Three applications are discussed. A known result about entropy production is reproduced. A thermodynamic relation is derived for equilibrium systems with Metropolis dynamics. Finally, a link is made with recent results concerning a one-dimensional polymer model.

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Jan Naudts, Erik Van der Straeten. 2008-10-23. Transition records of stationary Markov chains. https://doi.org/10.1103/physreve.74.040103

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