Role of network topology in non-equilibrium dynamics

Determine the role of network topology in the non-equilibrium dynamics of complex systems, specifically identifying how structural features of directed networks affect violations of detailed balance and entropy production across stochastic dynamical processes.

Background

The paper investigates how directedness and hierarchical organization in networks relate to broken detailed balance and entropy production for several dynamical processes (random walks, Ornstein–Uhlenbeck, and Ising dynamics). While it presents analytical and numerical evidence linking directedness to non-equilibrium behavior, it acknowledges that fully understanding the contribution of network topology to non-equilibrium dynamics remains unresolved.

This open problem is framed broadly and motivates the paper’s development of directedness measures (irreciprocity, trophic directedness, and non-normality) and its exploration of synthetic, empirical, and inferred networks. The authors’ results provide partial progress but do not close the question, highlighting the need for a comprehensive theory connecting topology to non-equilibrium thermodynamics.