Thermodynamics of precision: from counting statistics to clocks

Any clock is a nonequilibrium system that consumes and dissipates energy in order to produce an ordered sequence of ticks, which are counted by a register. A good clock produces ticks that are regularly spaced in time, so that the number of counts in a given time interval fluctuates little. The problem of timekeeping is thus intimately connected to the problem of full counting statistics in nonequilibrium systems. In this talk, I will show that quantum and stochastic thermodynamics impose fundamental bounds on the precision of timekeeping with nanoscale clocks. In particular, I will describe recent results showing that the precision of a clock scales with the rate at which it dissipates energy and is also bounded by its temporal resolution. These bounds are closely analogous to the thermodynamic and kinetic uncertainty relations that constrain biomolecular systems. I will present the recently discovered clock uncertainty relation, which yields the tightest bound on the fluctuations of any steady-state current in a classical stochastic system. I will explain how these stochastic uncertainty relations are modified in open quantum systems, which can exploit coherence and correlations to achieve higher precision. Finally, I will describe an experimental realisation of a nanoscale clock using a semiconducting device, which reveals that the thermodynamic cost of timekeeping arises not only from the resources needed to power the clock itself but also from the entropy produced during the measurement process.