Under stability, temperedness, and exponential cluster decomposition of the pair potential, the coarse-grained entropy of the N-body system satisfies S_CG = sum S_i plus an exponentially suppressed correction, recovering additivity in the thermodynamic limit.
Watanabe, Information theoretical analysis of multivariate correlation,IBM Journal of Research and Development,4(1960), 66–82
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Entropy additivity from exponential decay of correlations: a coarse-grained operator approach
Under stability, temperedness, and exponential cluster decomposition of the pair potential, the coarse-grained entropy of the N-body system satisfies S_CG = sum S_i plus an exponentially suppressed correction, recovering additivity in the thermodynamic limit.