Characterizing Activity in Driven Elastic Networks from the Non-equilibrium Scaling Behaviour

Detecting and quantifying non-equilibrium activity is essential for studying complex living systems such as cells. We present a non-invasive approach of measuring activity in a system based on the breaking of time-reversal symmetry. We focus on "cycling frequencies" - the frequencies with which the trajectories of pairs of degrees of freedom circle around in phase space, which is related to the entropy production rate. We test our approach on simple toy-models comprised of elastic networks immersed in a viscous fluid with spatially-varying internal driving. We prove both numerically and analytically that the cycling frequencies obey a power law as a function of distance between the selected degrees of freedom. Moreover, the behavior of the cycling frequencies contains information about the dimensionality of the system and the amplitude of active noise. Finally, we aim to find a mapping between the microscopic properties of a non-equilibrium system and macroscopic observables such as the cycling frequencies by including features such as the active force moments or spatial and temporal correlations of the active noise.