Abstract
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.
Highlights
Quantum systems provide the most accurate measurements of time [1,2,3], the concept of time in quantum theory remains elusive
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
We introduced the concept of autonomous quantum clocks to discuss these questions, and we argued that the measurement of time inevitably leads to an increase in entropy
Summary
Quantum systems provide the most accurate measurements of time [1,2,3], the concept of time in quantum theory remains elusive. The procedures of the state preparation and the measurement are usually not discussed explicitly These models allow one to measure a time interval, e.g., for implementing a given unitary operation (by timing an interaction). The pointer is designed to produce a sequence of signals, which are recorded by the register as ticks It follows that there is an asymmetric flow of information between the two parts of the clock, which makes the process irreversible (and singles out a direction for the flow of time). We make use of thermodynamical concepts in order to analyze the clock as an autonomous thermal machine [21,22,23], with the goal of producing a series of regular ticks This approach allows us to show that the clock’s irreversible entropy production dictates fundamental limits on its performance. We present a conjecture, backed up by general thermodynamic arguments, that such trade-offs are exhibited by any implementation of an autonomous clock
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