Time remains one of the least well-understood concepts in physics, most notably in quantum mechanics. A central goal is to find the fundamental limits of measuring time. One of the main obstacles is the fact that time is not an observable and thus has to be measured indirectly. Here, we explore these questions by introducing a model of time measurements that is complete and autonomous. Specifically, our autonomous quantum clock consists of a system out of thermal equilibrium—a prerequisite for any system to function as a clock—powered by minimal resources, namely, two thermal baths at different temperatures. Through a detailed analysis of this specific clock model, we find that the laws of thermodynamics dictate a trade-off between the amount of dissipated heat and the clock’s performance in terms of its accuracy and resolution. Our results furthermore imply that a fundamental entropy production is associated with the operation of any autonomous quantum clock, assuming that quantum machines cannot achieve perfect efficiency at finite power. More generally, autonomous clocks provide a natural framework for the exploration of fundamental questions about time in quantum theory and beyond.

1 aErker, Paul1 aMitchison, Mark, T.1 aSilva, Ralph1 aWoods, Mischa, P.1 aBrunner, Nicolas1 aHuber, Marcus uhttps://link.aps.org/doi/10.1103/PhysRevX.7.03102201441nas a2200205 4500008003900000022002500039245011200064210006900176490000700245520074100252653005500993653002001048100002301068700002701091700002501118700001701143700001801160700002101178856003601199 2016 d a2469-9950, 2469-996900aAutonomous {Quantum} {Refrigerator} in a {Circuit}-{QED} {Architecture} {Based} on a {Josephson} {Junction}0 aAutonomous Quantum Refrigerator in a Circuit QED Architecture Ba0 v943 aAn implementation of a small quantum absorption refrigerator in a circuit QED architecture is proposed. The setup consists of three harmonic oscillators coupled to a Josephson unction. The refrigerator is autonomous in the sense that it does not require any external control for cooling, but only thermal contact between the oscillators and heat baths at different temperatures. In addition, the setup features a built-in switch, which allows the cooling to be turned on and off. If timing control is available, this enables the possibility for coherence-enhanced cooling. Finally, we show that significant cooling can be achieved with experimentally realistic parameters and that our setup should be within reach of current technology.10aCondensed Matter - Mesoscale and Nanoscale Physics10aQuantum Physics1 aHofer, Patrick, P.1 aPerarnau-Llobet, Marti1 aBrask, Jonatan, Bohr1 aSilva, Ralph1 aHuber, Marcus1 aBrunner, Nicolas uhttp://arxiv.org/abs/1607.05218