# Scaling behavior of non-equilibrium measures in internally driven elastic assemblies

## TL;DR

This paper introduces a non-invasive method to quantify non-equilibrium activity in elastic assemblies by analyzing cycling frequencies, revealing their power-law behavior and dependence on system dimensionality and noise amplitude.

## Contribution

It establishes a theoretical and numerical framework linking cycling frequencies to non-equilibrium measures in elastic networks with internal activity.

## Key findings

- Cycling frequencies follow a power-law decay with distance.
- Behavior of cycling frequencies encodes system dimensionality.
- Analytical mapping predicts non-equilibrium measure behavior.

## Abstract

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.