Broken detailed balance and entropy production in directed networks

Nartallo-Kaluarachchi, Ramón; Asllani, Malbor; Deco, Gustavo; Kringelbach, Morten L.; Goriely, Alain; Lambiotte, Renaud

doi:http://dx.doi.org/10.1103/PhysRevE.110.034313

Broken detailed balance and entropy production in directed networks

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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

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.