  Clocks are inherently out-of-equilibrium because, due to friction, they
constantly consume free energy to keep track of time. The Thermodynamic
Uncertainty Relation (TUR) quantifies the trade-off between the precision of
any time-antisymmetric observable and entropy production. In the context of
clocks, the TUR implies that a minimum entropy production is needed in order to
achieve a certain level of precision in timekeeping. But the TUR has only been
proven for overdamped systems. Recently, a toy model of a classical underdamped
pendulum clock was proposed that violated this relation (Phys. Rev. Lett. 128,
130606), thus demonstrating that the TUR does not hold for underdamped
dynamics. We propose an electronic implementation of such a clock, using a
resistor-inductor-capacitor (RLC) circuit and a biased CMOS inverter (NOT
gate), which can work at different scales. We find that in the nanoscopic
single-electron regime of the circuit, we essentially recover the toy model
violating the TUR bound. However, in different macroscopic regimes of the
circuit, we show that the TUR bound is restored and analyze the thermodynamic
efficiency of timekeeping.
