  Fluctuations affect the functionality of nanodevices. Thermodynamic
uncertainty relations (TURs), derived within the framework of stochastic
thermodynamics, show that a minimal amount of dissipation is required to obtain
a given relative energy current dispersion, that is, current precision has a
thermodynamic cost. It is therefore of great interest to explore the
possibility that TURs are violated, particularly for quantum systems, leading
to accurate currents at lower cost. Here, we show that two quantum harmonic
oscillators are synchronized by coupling to a common thermal environment, at
strong dissipation and low temperature. In this regime, periodically modulated
couplings to a second thermal reservoir, breaking time-reversal symmetry and
taking advantage of non-Markovianity of this latter reservoir, lead to strong
violation of TURs for local work currents, while maintaining finite output
power. Our results pave the way for the use of synchronization in the
thermodynamics of precision.
