Theoretical modeling demonstrates an information-theoretic entropy balance in Markov chain Monte Carlo, indicating that acceptance decisions separate cooling from housekeeping circulation.
Markov chain Monte Carlo algorithms can be viewed as feedback devices that compare a proposed move with the target distribution and then accept or reject it. In this paper the Maxwell demon is identified with the acceptance module: it measures a proposed edge, stores the outcome in the accept/reject bit, and uses that bit to shape the probability current. The decision bit carries a genuine Shannon mutual information about the proposal, whereas only its directional part is converted into a cooling information flow. The relative-entropy relaxation rate obeys [Formula: see text], which separates useful cooling from housekeeping circulation in nonreversible chains.
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Masayuki Ohzeki (2026) studied this question.
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