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The accuracy of a clock can be tied to the entropy it creates

Today’s most advanced clocks save time with an incredibly accurate pace. But a new experiment suggests that the accuracy of clocks comes at a price: entropy.

Entropy or disorder is created every time you dial a clock. Now, scientists have measured the entropy generated by a clock that can run at different levels of accuracy. The more accurate the clock ticks are, the more entropy emitted, physicists report in an accepted article in Physical Review X.

“If you want a better watch, you have to pay for it,” says physicist Natalia Ares of Oxford University.

Time and entropy are closely intertwined concepts. Entropy is known as the “arrow of time,” because entropy tends to grow as time passes; the universe seems to move constantly from lower entropy to upper entropy (SN: 7/10/15). This march towards increasing entropy explains why some processes may advance in time but not the other way around: it is easy to mix cream into coffee but it is very difficult to separate it again. Machines also increase the disturbance when operating, for example, by releasing heat which increases the entropy of their environment. That means even a standard battery-powered watch produces entropy as it dials.

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Physicists had previously calculated that, for small quantum clocks, there is a direct relationship between the maximum possible accuracy of their ticks and the amount of entropy emitted. But larger clocks are too complex for these calculations. Therefore, it was not clear whether such a rule also applied to other types of watches.

To test the amount of entropy released in the tic-tac of a simplified clock, Ares and colleagues made a clock from a thin membrane, tens of nanometers thick and 1.5 millimeters long, suspended on two poles. An electrical signal sent to the clock propelled the membrane, causing it to flex up and down. This bending movement was repeated at regular intervals, as the constant ticks of a clock and an antenna recorded that movement. The more powerful the electrical signal, the more precisely it marked the clock. And as the accuracy of the clock increased, the entropy – the result of the heat produced in the antenna circuit – increased step by step.

That result suggests that the theoretical relationship of quantum clocks also applies to other types of clocks. "It's good to have that," says physicist Juan Parrondo of the Universidad Complutense de Madrid, who did not participate in the study. "What I'm not so sure about is how universal these kinds of relationships are." Researchers have studied only a variety of clocks. It’s still unclear whether the relationship between accuracy and entropy applies to clocks more generally, Parrondo says.

But some scientists suspect the relationship may be universal, revealing a key aspect of how watches work. The new study “would push us even further in this direction,” says quantum physicist Ralph Silva of ETH Zurich, who did not participate in the research. "It's a fact in favor that's probably the case with all watches. But that's not proven."

For a watch to work reliably, it must undergo a process that has a preferred direction over time. If the clock did not create entropy, it would be just as likely to run forward as backward. And the more entropy the clock creates, the less likely it is that the clock will fluctuate: temporary backward steps that would degrade its accuracy.

So, if the accuracy of all clocks has an increased cost of entropy, that compensation may reflect a close link between the passage of time and its measurement.

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