  When monitoring the dynamics of stochastic systems, such as interacting
particles agitated by thermal noise, disentangling deterministic forces from
Brownian motion is challenging. Indeed, we show that there is an
information-theoretic bound, the capacity of the system when viewed as a
communication channel, that limits the rate at which information about the
force field can be extracted from a Brownian trajectory. This capacity provides
an upper bound to the system's entropy production rate, and quantifies the rate
at which the trajectory becomes distinguishable from pure Brownian motion. We
propose a practical and principled method, Stochastic Force Inference, that
uses this information to approximate force fields and spatially variable
diffusion coefficients. It is data efficient, including in high dimensions,
robust to experimental noise, and provides a self-consistent estimate of the
inference error. In addition to forces, this technique readily permits the
evaluation of out-of-equilibrium currents and the corresponding entropy
production with a limited amount of data.
