The Arrow in the Cell

Play a video of a colloidal particle jiggling in water. Run it backwards. You can’t tell the difference. Brownian motion is time-reversible — the statistical properties of the trajectory look the same forwards and backwards. This is a consequence of thermal equilibrium: the fluctuation-dissipation theorem ensures that the particle’s kicks from the environment are balanced by its dissipation into the environment. No arrow of time.

Now put the particle inside a living cell. Play the video forward. Play it backwards. Knotz et al. (arXiv:2603.16517) show you can tell the difference. The cell breaks time-reversal symmetry.

The detection method uses mean back relaxation — a three-point correlation function that measures how a particle’s trajectory relates to its own past. In equilibrium, this correlation vanishes by construction: the past and future are statistically indistinguishable. In an active (non-equilibrium) system, the correlation is nonzero, and its magnitude quantifies how far the system is from equilibrium.

The experiment identifies the source. When microtubules are intact, the time-reversal asymmetry is strong. When microtubules are disrupted (by drug treatment), the asymmetry largely disappears. Microtubules are the highways along which molecular motors (kinesin, dynein) carry cargo. The motors consume ATP and generate directed forces — non-equilibrium driving that breaks the balance between fluctuation and dissipation. The particle in the cell feels these non-equilibrium forces, and its trajectory records the asymmetry.

The connection to thermodynamics is specific: the measured time-reversal asymmetry provides a lower bound on entropy production in the cell. The farther the system is from equilibrium, the more entropy it produces, and the more distinguishable forward from backward trajectories become. Active energies — previously measured from violations of the fluctuation-dissipation theorem — connect directly to this entropic arrow.

A colloidal particle in a cell is a thermometer for non-equilibrium. It measures, through its own jiggling, how alive the cell is.

Knotz, Muenker, Betz, & Krüger, “Time reversal breaking of colloidal particles in cells,” arXiv:2603.16517 (2026).