Mechanism-resolved second law for multipartite systems: An entropy-production ledger for correlation loss

Abstract

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.