Thermodynamic limit under Partial Observability

TL;DR

This paper derives a generalized second law of thermodynamics for multipartite systems under partial observability, linking entropy production to inaccessible correlations and emphasizing the role of information in thermodynamic processes.

Contribution

It introduces a new bound on entropy production considering only accessible correlations, refining existing thermodynamic limits without measurement updates.

Findings

Total entropy production is bounded by inaccessible correlation decrease.

Accessible correlations can be harnessed to reduce dissipation.

Unknown correlations inevitably lead to additional entropy production.

Abstract

We study thermodynamic limits when controllers operate with only partial observability of internal correlations in multipartite systems. Understanding the costs imposed by lack of information is crucial in settings where agents must act under incomplete knowledge, and clarifying the thermodynamics of the intertwined sense-act feedback remains a central challenge. We consider a single-step stochastic evolution of a classical multipartite system coupled to a single heat bath under protocols that do not generate new inter-subsystem correlations, and we allow arbitrary reciprocal interaction topology. From Clausius-type local inequalities for each component, we sum and recast the result into an information-theoretic form that isolates the role of inaccessible correlation changes. We thereby obtain a generalized second law: the total entropy production is bounded below exactly by the decrease of internal correlations that is inaccessible to any controller whose state is not included in the relevant information set; only the accessible part can, in principle, be diverted from dissipation. The result refines standard bounds without invoking measurement updates and characterizes information as an indispensable resource: correlations become work-relevant precisely to the extent that they are known, while the unknown portion is unavoidably dissipated.