  Detecting and quantifying non-equilibrium activity is essential for studying
internally driven assemblies, including synthetic active matter and complex
living systems such as cells or tissue. We discuss a non-invasive approach of
measuring non-equilibrium behavior based on the breaking of detailed balance.
We focus on "cycling frequencies" - the average frequency with which the
trajectories of pairs of degrees of freedom revolve in phase space, and explain
their connection with other non-equilibrium measures, including the area
enclosing rate and the entropy production rate. We test our approach on simple
toy-models comprised of elastic networks immersed in a viscous fluid with
site-dependent internal driving. We prove both numerically and analytically
that the cycling frequencies obey a power-law as a function of distance between
the tracked degrees of freedom. Importantly, the behavior of the cycling
frequencies contains information about the dimensionality of the system and the
amplitude of active noise. The mapping we use in our analytical approach thus
offers a convenient framework for predicting the behavior of two-point
non-equilibrium measures for a given activity distribution in the network.
