Transition records of stationary Markov chains
arXiv:cond-mat/0607485 · doi:10.1103/PhysRevE.74.040103
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.
arXiv commentcorrected error in the definition of the entropy production variable and in the proof of the fluctuation theorem
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- The 3-dimensional random walk with applications to overstretched DNA and the protein titin