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.7.03102201669nas a2200181 4500008003900000022001400039245007500053210006900128300001100197490000600208520111700214100002401331700001801355700001801373700002201391700002301413856005101436 2016 d a2058-956500aRealising a quantum absorption refrigerator with an atom-cavity system0 aRealising a quantum absorption refrigerator with an atomcavity s a0150010 v13 aAn autonomous quantum thermal machine comprising a trapped atom or ion placed inside an optical cavity is proposed and analysed. Such a machine can operate as a heat engine whose working medium is the quantised atomic motion or as an absorption refrigerator that cools without any work input. Focusing on the refrigerator mode, we predict that it is possible with state-of-the-art technology to cool a trapped ion almost to its motional ground state using a thermal light source such as sunlight. We nonetheless find that a laser or a similar reference system is necessary to stabilise the cavity frequencies. Furthermore, we establish a direct and heretofore unacknowledged connection between the abstract theory of quantum absorption refrigerators and practical sideband cooling techniques. We also highlight and clarify some assumptions underlying several recent theoretical studies on self-contained quantum engines and refrigerators. Our work indicates that cavity quantum electrodynamics is a promising and versatile experimental platform for the study of autonomous thermal machines in the quantum domain.1 aMitchison, Mark, T.1 aHuber, Marcus1 aPrior, Javier1 aWoods, Mischa, P.1 aPlenio, Martin, B. uhttp://stacks.iop.org/2058-9565/1/i=1/a=015001