TY - JOUR
T1 - Broken detailed balance and entropy production in directed networks
AU - Nartallo-Kaluarachchi, Ramón
AU - Asllani, Malbor
AU - Deco, Gustavo
AU - Kringelbach, Morten L.
AU - Goriely, Alain
AU - Lambiotte, Renaud
N1 - Publisher Copyright:
© 2024 authors. Published by the American Physical Society.
PY - 2024/9
Y1 - 2024/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85205017576&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.110.034313
DO - 10.1103/PhysRevE.110.034313
M3 - Journal article
AN - SCOPUS:85205017576
SN - 2470-0045
VL - 110
JO - Physical Review E
JF - Physical Review E
IS - 3
M1 - 034313
ER -