  The thermodynamic uncertainty relation offers a universal energetic
constraint on the relative magnitude of current fluctuations in nonequilibrium
steady states. However, it has only been derived for long observation times.
Here, we prove a recently conjectured finite-time thermodynamic uncertainty
relation for steady-state current fluctuations. Our proof is based on a
quadratic bound to the large deviation rate function for currents in the limit
of a large ensemble of many copies.
