Hierarchical Bounds on Entropy Production Inferred from Partial Information

TL;DR

This paper compares two methods for estimating total entropy production from partial observations, showing that the effective thermodynamics approach provides a more accurate lower bound and partitions entropy into observable and hidden contributions.

Contribution

The study demonstrates that the Polettini and Esposito scheme yields a better estimate of total entropy production and introduces a partitioning into observable and hidden parts satisfying fluctuation theorems.

Findings

Effective thermodynamics provides a tighter lower bound on entropy production.

Partitioning into observable and hidden entropy contributions satisfies fluctuation theorems.

The approach has broad implications for systems with limited information.

Abstract

Systems driven away from thermal equilibrium constantly deliver entropy to their environment. Determining this entropy production requires detailed information about the system's internal states and dynamics. However, in most practical scenarios, only a part of a complex experimental system is accessible to an external observer. In order to address this challenge, two notions of partial entropy production have been introduced in the literature as a way to assign an entropy production to an observed subsystem: one due to Shiraishi and Sagawa [Phys. Rev. E 91, 012130 (2015)] and another due to Polettini and Esposito [arXiv:1703.05715 (2017)]. We show that although both of these schemes provide a lower bound on the total entropy production, the latter -- which utilizes an effective thermodynamics description-- gives a better estimate of the total dissipation. Using this effective thermodynamic framework, we establish a partitioning of the total entropy production into two contributions that individually verify integral fluctuation theorems: an observable partial entropy production and a hidden entropy production assigned to the unobserved subsystem. Our results offer broad implications for both theoretical and empirical systems when only partial information is available.