Quantifying System‑Environment Synergistic Information by Effective Information Decomposition

Digital Technologies Research and Applications

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Quantifying System‑Environment Synergistic Information by Effective Information Decomposition

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https://doi.org/10.54963/dtra.v4i3.1492
Yang, M., Pan, L., & Zhang, J. (2025). Quantifying System‑Environment Synergistic Information by Effective Information Decomposition. Digital Technologies Research and Applications, 4(3), 22–34. https://doi.org/10.54963/dtra.v4i3.1492
Volume 4 Issue 3: December 2025 (In Progress)
Copyright (c) 2025 Mingzhe Yang, Linli Pan, Jiang Zhang
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Authors

  • Mingzhe Yang

    School of Systems Science, Beijing Normal University, Beijing 100875, China
  • Linli Pan

    School of Systems Science, Beijing Normal University, Beijing 100875, China
  • Jiang Zhang

    School of Systems Science, Beijing Normal University, Beijing 100875, China
    Swarma Research, Beijing 102300, China

Received: 3 August 2025; Revised: 27 August 2025; Accepted: 3 September 2025; Published: 29 September 2025

Living systems maintain structural and functional stability while adapting to environmental changes, a capability independent of specific system‑environment states. Existing frameworks, such as self‑organization theory and free energy principles, cannot measure system‑environment interaction at the causal level. In this article, we propose a new causal indicator, Flexibility, to measure a system’s ability to respond to its environment. We construct this indicator based on information theory and interventional operations from causal inference, which implies the indicator depends only on the dynamical causal mechanism. We show this indicator satisfies the axiom system of the partial information decomposition (PID) framework and decomposes into two components, Expansiveness and Introversion, which correspond to different strategic tendencies for environmental adaptation. This decomposition reveals that Flexibility depends on the entanglement between system‑environment variables and noise magnitude. Through experiments on cellular automata (CA), random Boolean networks, and real gene regulatory networks (GRNs), we validate that the indicator identifies the most complex and computationally capable CA (Langton’s parameter at 0.5), while demonstrating that feedback loops carrying important biological functions in GRNs exhibit the highest flexibility. We also find that flexibility peaks at a moderate level of dynamical noise. Furthermore, we combine this framework with machine learning techniques to demonstrate its applicability when the underlying dynamics are unknown.

Keywords:

Synergy Flexibility Effective Information Partial Information Decomposition Gene Regulatory Networks

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