SKM 2023 – scientific programme
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SYFP: Symposium Physics of Fluctuating Paths
SYFP 1: Physics of Fluctuating Paths
SYFP 1.5: Invited Talk
Tuesday, March 28, 2023, 11:45–12:15, HSZ 01
Thermodynamics of Clocks — •Patrick Pietzonka — Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
The thermodynamic uncertainty relation (TUR) establishes a seemingly universal trade-off between cost and precision for classical 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 2kBT. 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 inertia 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 . Beyond the minimal model, I also show numerically that the TUR can be broken in a fully continuous model with two underdamped degrees of freedom. Finally, I present a new bound valid for time-symmetric observables, which shows that for overdamped systems there is a minimal cost for producing a precise sequence of “ticks”.