  Thermodynamic uncertainty relations yield a lower bound on entropy production
in terms of the mean and fluctuations of a current. We derive their general
form for systems under arbitrary time-dependent driving from arbitrary initial
states and extend these relations beyond currents to state variables. The
quality of the bound is discussed for various types of observables for an
interacting pair of colloidal particles in a moving laser trap and for the
dynamical unfolding of a small protein. Since the input for evaluating these
bounds does not require specific knowledge of the system or its coupling to the
time-dependent control, they should become widely applicable tools for
thermodynamic inference in time-dependently driven systems.
