  We introduce an statistical mechanical formalism for the study of
discrete-time stochastic processes with which we prove: (i) General properties
of extremal chains, including triviality on the tail $\sigma$-algebra,
short-range correlations, realization via infinite-volume limits and
ergodicity. (ii) Two new sufficient conditions for the uniqueness of the
consistent chain. The first one is a transcription of a criterion due to
Georgii for one-dimensional Gibbs measures, and the second one corresponds to
Dobrushin criterion in statistical mechanics. (iii) Results on loss of memory
and mixing properties for chains in the Dobrushin regime. These results are
complementary of those existing in the literature, and generalize the Markovian
results based on the Dobrushin ergodic coefficient.
