Measuring and quantifying non-equilibrium dynamics in active biological systems is a major challenge, because of their intrinsic stochastic nature and the limited number of variables accessible in any real experiment. We investigate what non-equilibrium information can be extracted from non-invasive measurements using a stochastic model of soft elastic networks with a heterogeneous distribution of activities, representing enzymatic force generation. In particular, we use this model to study how the non-equilibrium activity, detected by tracking two probes in the network, scales as a function of the distance between the probes. We quantify the non-equilibrium dynamics through the cycling frequencies, a simple measure of circulating currents in the phase space of the probes. We find that these cycling frequencies exhibit power-law scaling behavior with the distance between probes. In addition, we show that this scaling behavior governs the entropy production rate that can be recovered from the two traced probes. Our results provide insight in to how internal enzymatic driving generates non-equilibrium dynamics on different scales in soft biological assemblies.