Contribution of modularity and small-worldness to entropy production

Ascertain the contribution of network modularity and small-worldness to the entropy production rate of dynamics on real-world directed networks, quantifying how these topological features influence broken detailed balance beyond measures of directedness.

Background

Analyzing 97 empirical directed networks, the paper finds strong correlations between non-normality and entropy production (especially for Ornstein–Uhlenbeck dynamics), but it also notes that real-world networks possess additional topological features, such as modularity and small-worldness, whose impact on entropy production is not established.

The authors suggest that these features may play a role in non-equilibrium dynamics and motivate further investigation, including null-modeling (directed configuration model) to disentangle topological effects.