arXiv subjects

Gabriel Knotz

Publications and source records attributed to Gabriel Knotz.

4 recordsLinked to original sources

arXiv2026

Time reversal breaking of colloidal particles in cells

We investigate signatures of broken time reversal symmetry in stochastic trajectory data, employing the previously introduced three point correlation called mean back relaxation. We specifically investigate data from a simple driven model, as well as from colloidal particles within living or passivated biological cells. Both in the model as well as in cell data, MBR detects broken time reversal symmetry, and furthermore, allows to determine relevant time and length scales of activity. For the cells, we show, by applying various drugs, that it is predominantly the presence of microtubules which is needed for a time reversal symmetry breaking. We employ a bound for entropy production, finding that it is in striking relation to previously determined active energies that quantify violation of the fluctuation dissipation theorem.

cond-mat.soft↗

arXiv2025

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

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.

cond-mat.stat-mech↗

arXiv2023

Mean Back Relaxation for Position and Densities

Correlation functions are a standard tool for analyzing statistical particle trajectories. Recently, a so called mean back relaxation (MBR) has been introduced, which correlates positions at three time points. The deviation of its long time value from $\frac{1}{2}$ has been shown to be a marker for breakage of time reversal symmetry for confined particles. Here, we extend the analysis of MBR in several ways, including discussion of a cut off length used when evaluating MBR from trajectory data. Using a path integral approach, we provide a general expression for MBR in terms of multipoint density correlations. For Gaussian systems, this expression yields a relation between MBR and mean squared displacement. We finally demonstrate that MBR can be applied to other stochastic observables besides particle position. Using it for microscopic densities, its deviation from $\frac{1}{2}$ is a marker for broken detailed balance in confinement or in bulk systems.

cond-mat.stat-mech↗

arXiv2023

Entropy bound for time reversal markers

We derive a bound for entropy production in terms of the mean of normalizable path-antisymmetric observables. The optimal observable for this bound is shown to be the signum of entropy production, which is often easier determined or estimated than entropy production itself. It can be preserved under coarse graining by use of a simple path grouping algorithm. We demonstrate this relation and its properties using a driven network on a ring, for which the bound saturates for short times for any driving strength. This work can open a way to systematic coarse graining of entropy production.

cond-mat.stat-mech↗