17.12.24 - Patrick Pietzonka "Thermodynamics of clocks"

Thermodynamics of clocks

 In order to break the time-reversal symmetry present at thermal equilibrium, any useful clock operating autonomously in a thermal environment needs to be driven by forces that ultimately lead to the production of entropy. This poses the question whether a minimal entropic cost is necessary for a clock to be reliable. The thermodynamic uncertainty relation (TUR) states that precision of any current-like observable in a non-equilibrium steady state is related to the entropy produced in the overall system. Applied to clocks, this would mean that the squared relative uncertainty of the displayed time multiplied by the energetic cost is always greater than 2kT.

 While the TUR has been proven for Markov jump processes and overdamped Brownian diffusion, a prove for systems involving inertia remained elusive. I will show an example of a clock that exploits inertia to break the TUR. It is modelled after a pendulum clock, consisting of an oscillator coupled to another degree of freedom acting as a counter.

 Finally, I will present a new entropic bound on precision, complementing the TUR for a class of time-symmetric observables that count the number of recurrences of some discrete event.