  The thermodynamic uncertainty relation (TUR) has been well studied for
systems with few degrees of freedom. While, in principle, the TUR holds for
more complex systems with many interacting degrees of freedom as well, little
is known so far about its behavior in such systems. We analyze the TUR in the
thermodynamic limit for mixtures of driven particles with short-range
interactions. Our main result is an explicit expression for the optimal
estimate of the total entropy production in terms of single-particle currents
and correlations between two-particle currents. Quantitative results for
various versions of a driven lattice gas demonstrate the practical
implementation of this approach.
