English

Transition records of stationary Markov chains

Statistical Mechanics 2009-11-11 v4

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.

Keywords

Cite

@article{arxiv.cond-mat/0607485,
  title  = {Transition records of stationary Markov chains},
  author = {Jan Naudts and Erik Van der Straeten},
  journal= {arXiv preprint arXiv:cond-mat/0607485},
  year   = {2009}
}

Comments

corrected error in the definition of the entropy production variable and in the proof of the fluctuation theorem