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Active Contact Forces Drive Non-Equilibrium Fluctuations in Membrane Vesicles

We analyze the non-equilibrium shape fluctuations of giant unilamellar vesicles encapsulating motile bacteria. Owing to bacteria--membrane collisions, we experimentally observe a significant increase in the magnitude of membrane fluctuations at low wave numbers, compared to the well-known thermal fluctuation spectrum. We interrogate these results by numerically simulating membrane height fluctuations via a modified Langevin equation, which includes bacteria--membrane contact forces. Taking advantage of the length and time scale separation of these contact forces and thermal noise, we further corroborate our results with an approximate theoretical solution to the dynamical membrane equations. Our theory and simulations demonstrate excellent agreement with non-equilibrium fluctuations observed in experiments. Moreover, our theory reveals that the fluctuation--dissipation theorem is not broken by the bacteria; rather, membrane fluctuations can be decomposed into thermal and active components.