A minimum entropy problem for stationary reversible stochastic spin systems on the infinite lattice (Q1891525)

The following problem is discussed. Suppose we are given a stochastic infinite spin-flip system, which is reversible with respect to a given Gibbs measure. The associated space-time empirical process satisfies a large deviation principle with a rate function that is a suitably defined entropy. The problem addressed here is to minimize such entropy over the class of those stationary processes having an assigned marginal. Under some conditions, an explicit expression for this minimum, and for the process that realizes it, is given.