Nonequilibrium dynamics of isostatic spring networks.

Marginally stable systems exhibit rich critical mechanical behavior. Such isostatic assemblies can be actively driven, but it is unclear how their critical nature affects their nonequilibrium dynamics. Here, we study the influence of isostaticity on the nonequilibrium dynamics of active spring networks. In our model, heterogeneously distributed white or colored, motorlike noise drives the system into a nonequilibrium steady state. We quantify the nonequilibrium dynamics of pairs of network nodes by the characteristic cycling frequency ω-an experimentally accessible measure of the circulation of the associated phase space currents. The distribution of these cycling frequencies exhibits critical scaling, which we approximately capture by a mean-field theory. Finally, we show that the scaling behavior of ω with distance is controlled by a diverging length scale. Overall, we provide a theoretical approach to elucidate the role of marginality in active disordered systems.