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The thermodynamic uncertainty relation (TUR) describes a trade-off relation between nonequilibrium currents and entropy production and serves as a fundamental principle of nonequilibrium thermodynamics. However, currently known TURs presuppose either specific initial states or an infinite-time average, which severely limits the range of applicability. #link# Here we derive a finite-time TUR valid for arbitrary initial states from the Cramér-Rao inequality. We find that the variance of an accumulated current is bounded from below by the
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