多体系统的机制分辨第二定律：关联损失的熵产生分类账
Mechanism-resolved second law for multipartite systems: An entropy-production ledger for correlation loss
AI总结：
该研究针对经典多体系统的关联损失问题，推导了适用于任意读取模式的精确熵产生分类账，得到机制分辨的第二定律，明确信息在功预算下决定访问权限而非代价，并提出单电子测试候选方案。
摘要：
在具有加和裸能量的多体系统中，子系统间的内部关联以每奈特$k_B T$的形式储存自由能。针对三个比特的三种单步过程可以具有相同的初末联合分布，但最小总熵产生有所不同，可为零或$\n 2$，这取决于导致关联损失的机制本身是否读取了承载该关联的变量。其中两类过程还可以共享其读取模式的有效声明以及每条轨迹上释放的热量，因此在该声明下计算的每阶段平衡和每个固定块模度值都一致；但其核的所有实现的最小总熵产生仍相差$\n 2$，这些核仅在全状态空间结构层面可区分。我们研究了与单一热库接触的经典多体系统的一个同步步骤。每个子系统由其自身的局域机制更新，该局域机制在局域细致平衡条件下读取其他子系统固定子集的步骤开始时快照。我们推导了一个适用于关联损失的精确熵产生分类账，该分类账对包括互易模式在内的任意读取模式均有效，且可通过显式过程达到饱和。在无环读取以及同一步骤内不会构建被擦除关联的协议下，该分类账退化为机制分辨的第二定律。总熵产生的下界为导致每次损失的机制所无法观测到的被破坏关联量。对于固定的转换任务，转换链上的有信息-无信息差距的上限为$k_B T$乘以初始总关联，且该上限是紧的。在单次运行的功预算下，信息决定的是访问权限而非代价。这种未被测量的差异为单电子测试提供了候选方案。
英文摘要：
Internal correlation among the subsystems of a many-body system with additive bare energies stores free energy at $k_B T$ per nat. Three one-step processes on three bits can share the same initial--final joint distribution yet differ in their minimum total entropy production, zero or $\ln 2$, depending on whether the mechanism causing the correlation loss itself reads the variable that carries it. Two such processes can further share a valid declaration of their reading patterns and the heat released on every trajectory, so that every per-stage balance and every fixed-block modularity value computed under that declaration coincides; the minimum total entropy production over implementations of their kernels still differs by $\ln 2$, the kernels remaining distinguishable only at the level of their full-state-space structure. We consider one synchronized step of a classical multipartite system in contact with a single heat bath. Each subsystem is updated by its own local mechanism, which reads a beginning-of-step snapshot of a fixed subset of the others under local detailed balance. We derive an exact entropy-production ledger for correlation loss that is valid for arbitrary reading patterns, including reciprocal ones, and is saturated by explicit processes. Under acyclic reading and for protocols that build no correlation erased within the same step, the ledger collapses to a mechanism-resolved second law. The total entropy production is bounded below by the destroyed correlation hidden from the mechanisms that caused each loss. For a fixed conversion task, the informed--blind gap along conversion chains is capped at $k_B T$ times the initial total correlation, and the cap is exact. Under a per-run work budget, information decides access rather than price. This unmeasured contrast identifies a candidate single-electron test.
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