Regensburg 2025 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 42: Stochastic Thermodynamics

DY 42.2: Talk

Friday, March 21, 2025, 09:45–10:00, H43

Staying on Time: Precision and Cost of a Controlled Clock — •Till Welker and Patrick Pietzonka — School of Physics and Astronomy, University of Edinburgh, United Kingdom

The precision of an autonomous clock is associated with an entropic cost. In overdamped systems, the precision-cost tradeoff is bounded by the thermodynamic uncertainty relation (TUR). To avoid paying immense costs while staying accurate over an extended period, the clocks in our phones, radios, and computers adapt their dynamics according to a precise reference clock.

We study the minimal model of the two-state controlled clock with one state running slower and one state running faster than the reference clock. At a rate R, the controlled clock reads out the reference clock and adjusts its state accordingly. While the clock hand progresses, the offset reaches an analytically solvable steady state, and the clock’s error remains bounded.

The combined cost of the controlled and reference clock obeys the TUR. However, the operator of the controlled clock only needs to pay a part of that cost, namely the driving of the controlled clock and the cost of state adjustment. We show that there is an R-dependent tradeoff between the controlled clock’s cost and its total error, and we explore the Pareto front of optimal clocks.

Keywords: Clocks; Thermodynamic Uncertainty Relation; Entropy Production