Title: Learning force fields from stochastic trajectories

Particles in biological and soft matter systems undergo Brownian dynamics: their deterministic motion, induced by forces, competes with random diffusion due to thermal noise. More broadly, Brownian dynamics is a generic and simple model for dynamical systems with noise. Provided only with the time-series of positions of such a system, i.e a trajectory in phase space, it is challenging to infer what force field had produced it. At the same time, this is the key information about the dynamical system, which would allow to characterize it completely. I will show that there is an information-theoretic bound on the rate at which information about the force field can be extracted from a trajectory, quantified by a channel capacity. I will discuss the relation between this capacity and the entropy production rate, as defined in stochastic thermodynamics. I will then present a practical method, Stochastic Force Inference, that uses the information contained in a trajectory to approximate force fields. This technique also permits the evaluation of out-of-equilibrium currents and entropy production. It thus makes it possible to quantify subtle time-irreversibility in biological systems at the mesoscale, and opens the door to an understanding of the importance of time- irreversibility.