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We present a numerical analysis of the entropy rate and statisticalcomplexity related to the spin flip dynamics of the 2D Ising Ferromagnet atdifferent temperatures T. We follow an information theoretic approach and testthree different entropy estimation algorithms to asses entropy rate andstatistical complexity of binary sequences. The latter are obtained bymonitoring the orientation of a single spin on a square lattice of side-lengthL=256 at a given temperature parameter over time. The different entropyestimation procedures are based on the M-block Shannon entropy (a wellestablished method that yields results for benchmarking purposes),non-sequential recursive pair substitution (providing an elaborate and anapproximate estimator) and a convenient data compression algorithm contained inthe zlib-library (providing an approximate estimator only). We propose anapproximate measure of statistical complexity that emphasizes on correlationswithin the sequence and which is easy to implement, even by means of black-boxdata compression algorithms. Regarding the 2D Ising Ferromagnet simulated usingMetropolis dynamics and for binary sequences of finite length, the proposedapproximate complexity measure is peaked close to the critical temperature. Forthe approximate estimators, a finite-size scaling analysis reveals that thepeak approaches the critical temperature as the sequence length increases.Results obtained using different spin-flip dynamics are briefly discussed. Thesuggested complexity measure can be extended to non-binary sequences in astraightforward manner.

A computational mechanics approach to estimate entropy and (approximate) complexity for the dynamics of the 2D Ising Ferromagnet