For any two-dimensional nearest neighbor shift of finite type X and anyinteger n > 0, one can define the horizontal strip shift H_n(X) to be the setof configurations on Z x {1,...,n} which do not contain any forbiddentransitions for X. It is always the case that the sequence h(H_n(X))/n ofnormalized topological entropies of the strip shifts approaches h(X), thetopological entropy of X. In this paper, we use probabilistic methods frominteracting particle systems to show that for the two-dimensional hard squareshift H, in fact h(H_{n+1}(H)) - h(H_n(H)) also approaches h(H), and the rateof convergence is at least exponential. A consequence of this is that h(H) iscomputable to any tolerance 1/n in time polynomial in n. We also give anexample of a two-dimensional block gluing nearest neighbor shift of finite typeY for which h(H_{n+1}(Y)) - h(H_n(Y)) does not even approach a limit.
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