Non-Markovian dynamics of a torsion pendulum immersed in an active bath

A torsion pendulum can probe a variety of phenomena such as photon spin or gravity, uncover the properties of spider draglines or examine stochastic thermodynamics of driven systems. Here we use such a device to probe the state of an assembly of macroscopic self propelled rod-like robots, a system that is out of equilibrium and very sensitive to the surrounding boundaries. When the persistent motion of the active particles plays an important role or when the particle assembly becomes dense, the probe dynamics shows non Markovian behaviour, i.e. memory effects, and a Gaussian but exponentially correlated noise arises. The correlation time of this active noise increases with the number of particles and undergoes a large jump when a transition to cluster formation occurs. The system allows direct tests of fluctuation theorems for second order Langevin equations with correlated noise. Effective temperatures are then obtained for a wide range of particle densities including the range where clusters dominate the dynamics. Torsion pendulums are versatile tools for exploring complex systems, including those out of equilibrium. The authors investigate macroscopic selfpropelled rod-like robots, revealing non-Markovian dynamics and exponentially correlated noise, with implications for understanding active matter and testing fluctuation theorems in dense particle assemblies.