Evaluating non-equilibrium trajectories via mean back relaxation: Dependence on length and time scales

TL;DR

This paper investigates how mean back relaxation (MBR) depends on length and time scales in biological and model systems, extending previous relations and analyzing variance to understand non-Gaussian dynamics.

Contribution

It extends the analysis of MBR and its relation to effective energy over broader parameters and compares experimental data with Gaussian models to reveal non-Gaussian behavior.

Findings

Qualitative agreement between cell and model systems for MBR dependence.

Extended the MBR-effective energy relation to larger time ranges.

Identified non-Gaussian dynamics through variance analysis.

Abstract

The mean back relaxation (MBR) relates the value of a stochastic process at three different time points. It has been shown to detect broken detailed balance under certain conditions. For experiments of probe particles in living and passivated cells, MBR was found to be related to the so called effective energy, which quantifies the violation of the fluctuation dissipation theorem. In this manuscript, we discuss the dependence on the length and time parameters that enter MBR, both for cells as well as for a model system, finding qualitative agreement between the two. For the cell data, we extend the phenomenological relation between MBR and effective energy to a larger range of time parameters compared to previous work, allowing to test it in systems with limited resolution. We analyze the variance of back relaxation (VBR) in dependence of the mentioned parameters, relevant for the statistical error in MBR evaluation. For Gaussian systems, the variance is found analytically in terms of the mean squared displacement, and we determine its absolute minimum as a function of the length and time parameters. Comparing VBR from cell data to a Gaussian prediction demonstrates a non-Gaussian process.