Abstract

I will briefly review the basic ideas behind the thermodynamic uncertainty relation (TUR). It establishes a seemingly universal trade-off between cost and precision for non-equilibrium systems in a steady state. Applied to clocks subject to thermal noise, it states that the product of the energy used for the driving and the squared relative uncertainty of the displayed time is always greater than 2kT. The TUR has been proven for models based on Markov jump dynamics or overdamped Brownian motion. It had also been conjectured to hold for underdamped Brownian dynamics, i.e., systems where inertial plays a role. This conjecture can now be disproven. I will present a counterexample that is inspired by a pendulum clock, consisting of an underdamped oscillator and a discrete counter, with thermal noise accounted for in both degrees of freedom. As it turns out analytically, this classic design principle of a clock allows one to overcome the bounds on precision set by the TUR . Finally, I will also show numerically that the TUR can be broken in a fully continuous model with two underdamped degrees of freedom.

The talk is based on: Phys. Rev. Lett. 128, 130606 (2022)