Effective temperature and dissipation of a gas of active particles probed by the vibrations of a flexible membrane

Abstract

We use a flexible circular membrane to probe a gas of macroscopic self-propelled rod-like robots. The fluctuations of the membrane are completely described by a set of discrete modes with different characteristic frequencies. We show that the dynamics of each mode can be well described by a Langevin equation with a white noise and a frequency-independent dissipation. This allows to extract the dissipation and fluctuation intensity for each mode, and consequently the contribution to the dissipation due to the collisions with the gas. The ratio of the gas-generated fluctuation and dissipation does not depend on the mode, indicating that the system interacts with the membrane as an equilibrium environment at a given effective temperature. We also find that this effective temperature coincides with the average kinetic energy of the rod-like robots. Quite surprisingly, this study thus shows that in a wide range of densities and frequencies the behavior of self-propelled robots can be regarded as that of an equilibrium gas. The method is quite general, and can be used to unveil deviations from this simple behavior in other regimes.