  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.
