Title: Finite-time generalization of the thermodynamic uncertainty relation,
Abstract: For fluctuating currents in non-equilibrium steady states, the recently
discovered thermodynamic uncertainty relation expresses a fundamental relation
between their variance and the overall entropic cost associated with the
driving. We show that this relation holds not only for the long-time limit of
fluctuations, as described by large deviation theory, but also for fluctuations
on arbitrary finite time scales. This generalization facilitates applying the
thermodynamic uncertainty relation to single molecule experiments, for which
infinite timescales are not accessible. Importantly, often this finite-time
variant of the relation allows inferring a bound on the entropy production that
is even stronger than the one obtained from the long-time limit. We illustrate
the relation for the fluctuating work that is performed by a stochastically
switching laser tweezer on a trapped colloidal particle.