马尔可夫链蒙特卡洛中的麦克斯韦妖：冷却信息流与熵平衡
Maxwell's Demon in Markov Chain Monte Carlo: Cooling Information Flow and Entropy Balance
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中文总结 AI 辅助
本文将麦克斯韦妖对应于马尔可夫链蒙特卡洛的接受模块，推导了相对熵弛豫速率公式，实现了非可逆链中冷却过程与内务循环的分离。
中文摘要 AI 辅助
马尔可夫链蒙特卡洛（MCMC）算法可被视为反馈装置，其会将提议的移动与目标分布进行比较，随后接受或拒绝该移动。本文将麦克斯韦妖识别为接受模块：它测量提议的边，将结果存储在接受/拒绝位中，并利用该位塑造概率流。决策位携带关于提议的真实香农互信息，而仅其方向部分被转换为冷却信息流。相对熵弛豫速率满足 $v(t)=\dot{\mathcal I}_{\rm cool}(t)+\dot S(t)$，该式在非可逆链中将有用的冷却过程与内务循环分离开来。
英文摘要
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 $v(t)=\dot{\mathcal I}_{\rm cool}(t)+\dot S(t)$, which separates useful cooling from housekeeping circulation in nonreversible chains.
