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Geometric decomposition of information flow: New insights into information thermodynamics

Yoh Maekawa1,*, Ryuna Nagayama1, Kohei Yoshimura2,3, and Sosuke Ito1,3,†

  • 1Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • 2Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, Pioneering Research Institute (PRI), RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
  • 3Universal Biology Institute, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

  • *Contact author: yoh.maekawa@ubi.s.u-tokyo.ac.jp
  • †Contact author: sosuke.ito@ubi.s.u-tokyo.ac.jp
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Phys. Rev. Research 8, 023292 – Published 15 June, 2026

DOI: https://doi.org/10.1103/trrq-tkw5

Abstract

We propose a decomposition of information flow into housekeeping and excess components for autonomous bipartite systems described by Markov jump processes. We introduce this decomposition using the geometric structure of probability currents and the conjugate thermodynamic forces. The housekeeping component arises from cyclic modes caused by violations of detailed balance and maintains the correlations between the two subsystems. In contrast, the excess component arises from conservative forces and alters the mutual information between the two subsystems. With this decomposition, we generalize previous results, such as the second law of information thermodynamics, the cyclic decomposition, and the information-thermodynamic extensions of thermodynamic trade-off relations.

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Phys. Rev. Research 8, 023292– Published 15 June, 2026
  • Received 31 October 2025
  • Accepted 19 May 2026
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