  In this paper, we develop a general theory for the estimation of the
transition probabilities of reversible Markov chains using the maximum entropy
principle. A broad range of physical models can be studied within this
approach. We use one-dimensional classical spin systems to illustrate the
theoretical ideas. The examples studied in this paper are: the Ising model, the
Potts model and the Blume-Emery-Griffiths model.
