Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Correspondence
  • Published:

Disentangling high-order mechanisms and high-order behaviours in complex systems

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Contrasting high-order mechanisms and behaviours in complex systems.


  1. Battiston, F. et al. Nat. Phys. 17, 1093–1098 (2021).

    Article  Google Scholar 

  2. Watanabe, S. IBM J. Res. Dev. 4, 66–82 (1960).

    Article  Google Scholar 

  3. Gat, I. & Tishby, N. in Adv. Neural Inf. Process. Syst (eds Kearns, M. J. et al.) 111–117 (MIT Press, 1999).

  4. Tononi, G., Sporns, O. & Edelman, G. M. Proc. Natl Acad. Sci. USA 91, 5033–5037 (1994).

    Article  ADS  Google Scholar 

  5. Williams, P. L. & Beer, R. D. Preprint at (2010).

  6. Lizier, J. T., Bertschinger, N., Jost, J. & Wibral, M. Entropy 20, 307 (2018).

    Article  ADS  Google Scholar 

  7. Mediano, P. A. et al. Preprint at (2021).

  8. Battiston, F. et al. Phys. Rep. 874, 1–92 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  9. Peixoto, T. P. Phys. Rev. Lett. 123, 128301 (2019).

    Article  ADS  Google Scholar 

  10. Matsuda, H. Phys. Rev. E 62, 3096 (2000).

    Article  ADS  Google Scholar 

Download references


F.R. was supported by the Ad Astra Chandaria Foundation. P.M. was funded by the Wellcome Trust (grant no. 210920/Z/18/Z). A.L. was supported by a Gates Cambridge Scholarship (OPP1144). T.V. is supported by the NSF-NRT grant 1735095, Interdisciplinary Training in Complex Networks and Systems at Indiana University Bloomington. S.S. was supported by the Italian MIUR PRIN 2017 (2017WZFTZP). A.L. and T.V. gratefully acknowledge the support of a Young Researchers’ Bridge Grant from the Complex Systems Society.

Author information

Authors and Affiliations


Corresponding authors

Correspondence to Fernando E. Rosas, Pedro A. M. Mediano or Andrea I. Luppi.

Ethics declarations

Competing interests

The authors declare no competing interests.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rosas, F.E., Mediano, P.A.M., Luppi, A.I. et al. Disentangling high-order mechanisms and high-order behaviours in complex systems. Nat. Phys. 18, 476–477 (2022).

Download citation

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing