Broken detailed balance and entropy production in directed networks

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  • dc.contributor.author Nartallo-Kaluarachchi, Ramón
  • dc.contributor.author Asllani, Malbor
  • dc.contributor.author Deco, Gustavo
  • dc.contributor.author Kringelbach, Morten L.
  • dc.contributor.author Goriely, Alain
  • dc.contributor.author Lambiotte, Renaud
  • dc.date.accessioned 2025-06-19T09:07:52Z
  • dc.date.available 2025-06-19T09:07:52Z
  • dc.date.issued 2024
  • dc.description.abstract The structure of a complex network plays a crucial role in determining its dynamical properties. In this paper, we show that the the degree to which a network is directed and hierarchically organized is closely associated with the degree to which its dynamics break detailed balance and produce entropy. We consider a range of dynamical processes and show how different directed network features affect their entropy production rate. We begin with an analytical treatment of a two-node network followed by numerical simulations of synthetic networks using the preferential attachment and Erdös-Renyi algorithms. Next, we analyze a collection of 97 empirical networks to determine the effect of complex real-world topologies. Finally, we present a simple method for inferring broken detailed balance and directed network structure from multivariate time series and apply our method to identify non-equilibrium dynamics and hierarchical organisation in both human neuroimaging and financial time series. Overall, our results shed light on the consequences of directed network structure on non-equilibrium dynamics and highlight the importance and ubiquity of hierarchical organisation and non-equilibrium dynamics in real-world systems.
  • dc.description.sponsorship The authors wish to acknowledge M. Aguilera for his assistance understanding the Ising mean-field approximation and R. MacKay for his comments on the manuscript. R.N.K was supported by an Engineering Physical Sciences Research Council (EPSRC) Doctoral Scholarship from Grants No. EP/T517811/1 and No. EP/R513295/1. G.D. was supported by the AGAUR research support grant (ref. 2021 SGR 00917) funded by the Department of Research and Universities of the Generalitat of Catalunya, by the project NEurological MEchanismS of Injury, and the project Sleep-like cellular dynamics (NEMESIS) (ref. 101071900) funded by the EU Horizon EUROPE European Research Council (ERC) Synergy Horizon Europe and by the Project No. PID2022-136216NB-I00 financed by the MCIN /AEI /10.13039/501100011033 / FEDER, UE., the Ministry of Science and Innovation, the State Research Agency and the European Regional Development Fund. M.L.K was supported by the Centre for Eudaimonia and Human Flourishing funded by the Pettit and Carlsberg Foundations and by the Center for Music in the Brain (MIB), funded by the Danish National Research Foundation (Project No. DNRF117). R.L. was supported by the EPSRC Grants No. EP/V013068/1 and No. EP/V03474X/1.
  • dc.format.mimetype application/pdf
  • dc.identifier.citation Nartallo-Kaluarachchi R, Asllani M, Deco G, Kringelbach ML, Goriely A, Lambiotte R. Broken detailed balance and entropy production in directed networks. Phys Rev E. 2024 Sep;110:034313. DOI: 10.1103/PhysRevE.110.034313
  • dc.identifier.doi http://dx.doi.org/10.1103/PhysRevE.110.034313
  • dc.identifier.issn 2470-0045
  • dc.identifier.uri http://hdl.handle.net/10230/70728
  • dc.language.iso eng
  • dc.publisher American Physical Society
  • dc.relation.ispartof Physical Review E. 2024 Sep;110:034313
  • dc.relation.projectID info:eu-repo/grantAgreement/EC/HE/101071900
  • dc.relation.projectID info:eu-repo/grantAgreement/ES/3PE/PID2022-136216NB-I00
  • dc.rights Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. . Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
  • dc.rights.accessRights info:eu-repo/semantics/openAccess
  • dc.rights.uri http://creativecommons.org/licenses/by/4.0/
  • dc.subject.other Xarxes
  • dc.subject.other Equilibri termodinàmic
  • dc.subject.other Entropia
  • dc.title Broken detailed balance and entropy production in directed networks
  • dc.type info:eu-repo/semantics/article
  • dc.type.version info:eu-repo/semantics/publishedVersion

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