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Biological assemblies such as chromosomes, membranes, and the cytoskeletonare driven out of equilibrium at the nanoscale by enzymatic activity andmolecular motors. Similar non-equilibrium dynamics can be realized in syntheticsystems, such as chemically fueled colloidal particles. Characterizing thestochastic non-equilibrium dynamics of such active soft assemblies stillremains a challenge. Recently, new non-invasive approaches have been proposedto determine non-equilibrium behavior, which are based on detecting brokendetailed balance in the stochastic trajectories of several coordinates of thesystem. Inspired by the method of two-point microrheology, in which theequilibrium fluctuations of a pair of probe particles reveal the viscoelasticresponse of an equilibrium system, here we investigate whether we can extendsuch an approach to non-equilibrium assemblies: can one extract information onthe nature of the active driving in a system from the analysis of a two-pointnon-equilibrium measure? We address this question theoretically in the contextof a class of elastic systems, driven out of equilibrium by a spatiallyheterogeneous stochastic internal driving. We consider several scenarios forthe spatial features of the internal driving that may be relevant in biologicaland synthetic systems, and investigate how such features of the active noisemay be reflected in the long-range scaling behavior of two-pointnon-equilibrium measures.

Mesoscopic non-equilibrium measures can reveal intrinsic features of the active driving