For a system which may be partitioned into M subsystems A1, A2, …, AM, such that configurations of subsystems Ai, Aj correspond to realizations of discrete, random variables si, sj, not necessarily isomorphic, and such that the probability for a configuration of the total system is p(s1, s2, …, sM) = f1(s1) … fM(sM)g1(s1, s2) × g2(s2, s3) … gM−1(sM−1, sM), we prove that p(s1, s2, …, sM) = p1(s1 | s2)p2(s2 | s3) … pM−1(sM−1 | sM)pM(sM), where pi(si | si+1) is the conditional probability for si given si+1, and pi(si) is the reduced probability for si. This result yields a decomposition of the total entropy into ``single‐subsystem entropies'' −Σ pi(si) lnpi(si) and ``nearest‐neighbor'' cumulant‐like terms −Σpj(sj,sj+1) ln[pj(sj,sj+1)/pj(sj)pj+1(sj+1)] only. This Markovian decomposition applies to systems with short‐range interactions for which transfer‐matrix methods are introduced.

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