Broken detailed balance and entropy production in directed networks
arxiv(2024)
摘要
The structure of a complex network plays a crucial role in determining its
dynamical properties. In this work, we show that the directed, hierarchical
organisation of a network causes the system to break detailed balance and
dictates the production of entropy through non-equilibrium dynamics. We
consider a wide range of dynamical processes and show how different directed
network features govern their thermodynamics. Next, we analyse a collection of
97 empirical networks and show that strong directedness and non-equilibrium
dynamics are both ubiquitous in real-world systems. 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 and hierarchical organisation in both human neuroimaging and
financial time-series. Overall, our results shed light on the thermodynamic
consequences of directed network structure and indicate the importance and
ubiquity of hierarchical organisation and non-equilibrium dynamics in
real-world systems.
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