Nartallo-Kaluarachchi, RamónAsllani, MalborDeco, GustavoKringelbach, Morten L.Goriely, AlainLambiotte, Renaud2025-06-192025-06-192024Nartallo-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.110.0343132470-0045http://hdl.handle.net/10230/70728The 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.application/pdfengPublished 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.XarxesEquilibri termodinàmicEntropiainfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevE.110.034313info:eu-repo/semantics/openAccess