  We introduce an example of thermodynamic uncertainty relation (TUR) for
systems modeled by a one-dimensional generalised Langevin dynamics with memory,
determining the motion of a micro-bead driven in a complex fluid. Contrary to
TURs typically discussed in the previous years, our observables and the entropy
production rate are one-time variables. The bound to the signal-to-noise ratio
of such state-dependent observables only in some cases can be mapped to the
entropy production rate. For example, this is true in Markovian systems. Hence,
the presence of memory in the system complicates the thermodynamic
interpretation of the uncertainty relation.
