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

## TL;DR

This paper explores how mesoscopic non-equilibrium measures can reveal intrinsic features of active driving in biological and synthetic systems by analyzing stochastic trajectories and broken detailed balance.

## Contribution

It extends two-point microrheology methods to non-equilibrium systems, analyzing how active noise features influence long-range scaling behavior.

## Key findings

- Two-point non-equilibrium measures reflect active noise characteristics.
- Different spatial features of internal driving alter long-range scaling.
- Theoretical framework applicable to biological and synthetic active systems.

## Abstract

Biological assemblies such as chromosomes, membranes, and the cytoskeleton are driven out of equilibrium at the nanoscale by enzymatic activity and molecular motors. Similar non-equilibrium dynamics can be realized in synthetic systems, such as chemically fueled colloidal particles. Characterizing the stochastic non-equilibrium dynamics of such active soft assemblies still remains a challenge. Recently, new non-invasive approaches have been proposed to determine non-equilibrium behavior, which are based on detecting broken detailed balance in the stochastic trajectories of several coordinates of the system. Inspired by the method of two-point microrheology, in which the equilibrium fluctuations of a pair of probe particles reveal the viscoelastic response of an equilibrium system, here we investigate whether we can extend such an approach to non-equilibrium assemblies: can one extract information on the nature of the active driving in a system from the analysis of a two-point non-equilibrium measure? We address this question theoretically in the context of a class of elastic systems, driven out of equilibrium by a spatially heterogeneous stochastic internal driving. We consider several scenarios for the spatial features of the internal driving that may be relevant in biological and synthetic systems, and investigate how such features of the active noise may be reflected in the long-range scaling behavior of two-point non-equilibrium measures.