Influence of hierarchically modular structure on non-equilibrium dynamics

Elucidate how hierarchically modular network structure influences non-equilibrium dynamics and entropy production in complex systems, extending findings that such structure affects critical dynamics to the context of broken detailed balance.

Background

The paper links directedness and hierarchical organization to non-equilibrium behavior, and notes parallels with prior work showing that hierarchically modular structure strongly impacts critical dynamics. It emphasizes that the effect of hierarchical modularity on non-equilibrium (entropy-producing) dynamics has not been clarified.

This problem seeks to bridge the gap between critical phenomena and stochastic thermodynamics on complex networks, potentially informing how specific multi-scale structures modulate irreversibility and entropy production in real systems.