Decoding active force fluctuations from spatial trajectories of active systems

Mesoscopic active systems exhibit various unique behaviors-absent in passive systems-due to the forces generated by the corresponding constituents by converting their available free energies. However, estimating these forces-which are also stochastic and remain intertwined with the thermal noise-is especially nontrivial. Here, we introduce a technique to extract such fluctuating active forces acting on a passive particle immersed in an active bath with high statistical accuracy by filtering out the related thermal noise. We first test the efficacy of our method under numerical scenarios with different types of activity, and then apply it to the experimental trajectories of a microscopic particle (optically) trapped inside an active bath consisting of motile E. coli bacteria. We believe that our simple yet powerful approach, which appears agnostic to the nature of the active force, should enable accurate measurement of force dynamics in living matter and potentially allow direct but reliable estimation of key thermodynamic parameters, such as heat, work, and entropy production.