Information Exchange Fluctuation Theorem Under Coarse-Graining

Lee Jinwoo ()
Additional contact information
Lee Jinwoo: Department of Mathematics, Kwangwoon University, 20 Kwangwoon-ro, Seoul 01897, Republic of Korea

Mathematics, 2025, vol. 13, issue 16, 1-13

Abstract: The fluctuation theorem for information exchange, originally established by Sagawa and Ueda, provides a fundamental framework for understanding the role of correlations in coupled classical stochastic systems. Building upon this foundation, Jinwoo demonstrated that the pointwise mutual information between correlated subsystems captures entropy production as a state function during coupling processes. In this study, we investigate the robustness of this information-theoretic fluctuation theorem under coarse-graining in coupled classical fluctuating systems. We rigorously prove that the fluctuation theorem remains invariant under arbitrary coarse-graining transformations and derive hierarchical relationships between information measures across different scales, thereby establishing its fundamental character as independent of the level of system description. Our results demonstrate that the relationship between information exchange and entropy production is preserved across different scales of observation, providing deeper insights into the thermodynamic foundations of information processing in classical stochastic systems.

Keywords: local non-equilibrium thermodynamics; fluctuation theorem; mutual information; entropy production; pointwise mutual information; thermodynamics of information; stochastic thermodynamics; weak coupling approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/16/2607/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/16/2607/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:16:p:2607-:d:1724685

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().