  The thermodynamic uncertainty relation originally proven for systems driven
into a non-equilibrium steady state (NESS) allows one to infer the total
entropy production rate by observing any current in the system. This kind of
inference scheme is especially useful when the system contains hidden degrees
of freedom or hidden discrete states, which are not accessible to the
experimentalist. A recent generalization of the thermodynamic uncertainty
relation to arbitrary time-dependent driving allows one to infer entropy
production not only by measuring current-observables but also by observing
state variables. A crucial question then is to understand which observable
yields the best estimate for the total entropy production. In this paper we
address this question by analyzing the quality of the thermodynamic uncertainty
relation for various types of observables for the generic limiting cases of
fast driving and slow driving. We show that in both cases observables can be
found that yield an estimate of order one for the total entropy production. We
further show that the uncertainty relation can even be saturated in the limit
of fast driving.

Statistical Mechanics