Non-equilibrium dynamics of isostatic spring networks

Mechanical systems exhibit rich critical behavior in the vicinity of the isostatic point. Inspired by living matter such as cytoskeletal networks and tissue, we here consider marginal assemblies driven out of equilibrium by internal activity. To date it remains unclear how the critical nature of such systems affects their non-equilibrium dynamics. We elucidate the role of the isostatic threshold in active diluted spring networks: heterogeneously distributed active noise sources drive the system into a non-equilibrium steady state. The non-equilibrium dynamics between pairs of network nodes are quantified by the characteristic cycling frequency ω—a measure of the circulation of the associated phase space currents. We reveal critical scaling of the cycling frequencies and intuitively understand their local behavior employing a mean-field approach. Overall, our work serves as a bridge connecting the well-established theory of mechanical stability to the novel field of non-equilibrium statistical mechanics.