Computing bounds for entropy of stationary Z^d Markov random fields
  For any stationary $\mZ^d$-Gibbs measure that satisfies strong spatial mixing, we obtain sequences of upper and lower approximations that converge to its entropy. In the case, $d=2$, these approximations are efficient in the sense that the approximations are accurate to within $\epsilon$ and can be computed in time polynomial in $1/\epsilon$. 
Brian Marcus, Ronnie Pavlov
math.DS math-ph math.MP math.PR