At a quantum critical point (QCP)--a zero-temperature singularity in which a line of continuous phase transition terminates--quantum fluctuations diverge in space and time, leading to exotic phenomena that can be observed at nonzero temperatures. Using a quantum antiferromagnet, we present calorimetric evidence that nuclear spins frozen in a high-temperature nonequilibrium state by temperature quenching are annealed by quantum fluctuations near the QCP. This phenomenon, with readily detectable heat release from the nuclear spins as they are annealed, serves as an excellent marker of a quantum critical region around the QCP and provides a probe of the dynamics of the divergent quantum fluctuations.
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