  We examine the so-called thermodynamic uncertainty relation (TUR), a
cost-precision trade-off relationship in transport systems. Based on the
fluctuation symmetry, we derive a condition on the validity of the TUR for
general nonequilibrium (classical and quantum) systems. We find that the first
non-zero contribution to the TUR beyond equilibrium, given in terms of
nonlinear transport coefficients, can be positive or negative, thus affirming
or violating the TUR depending on the details of the system. We exemplify our
results for noninteracting quantum systems by deriving the thermodynamic
uncertainty relation in the language of the transmission function. We
demonstrate that quantum coherent systems that do not follow a population
Markovian master equation, e.g. by supporting high order tunneling processes or
relying on coherences, violate the TUR.
