  We present a general way of quantifying the entropic uncertainty of quantum
field configurations in phase space in terms of entropic distinguishability
with respect to the vacuum. Our approach is based on the functional Husimi
$Q$-distribution and a suitably chosen relative entropy, which we show to be
non-trivially bounded from above by the uncertainty principle. The resulting
relative entropic uncertainty relation is as general as the concept of coherent
states and thus holds for quantum fields of bosonic and fermionic type. Its
simple form enables diverse applications, among which we present a complete
characterization of the uncertainty surplus of arbitrary states in terms of the
total particle number for a scalar field and the fermionic description of the
Ising model. Moreover, we provide a quantitative interpretation of the role of
the uncertainty principle for quantum phase transitions.
