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The Deeper Cost of Timekeeping Accuracy

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Keeping time accurately comes at a price; the maximum accuracy of a clock is directly related to how much disorder, or entropy, it creates in the universe every time it ticks.

This discovery was the result of work by Natalia Ares at the University of Oxford and her colleagues using a tiny clock with an accuracy that can be controlled. The clock itself was a 50-nanometre-thick membrane of silicone nitride, vibrated by an electric current. Each time the moved up and down once, and then returned to its original position, a tick was counted. The regularity of the spacing between the ticks was used as the measure of the clock’s accuracy.

The researchers found that as they increased the clock’s accuracy, the heat generated in the system also grew, increasing the entropy of its surroundings by jostling against nearby particles. According to Ares, “If a clock is more accurate, you are paying for it somehow.” In this case, the price is paid when you pour more ordered energy into the clock which is then converted into entropy. According to Ares, “By measuring time, we are increasing the entropy of the universe”, and the more entropy in the universe, the closer it may be to its eventual demise. “Maybe we should stop measuring time,” muses Ares, but she concludes that the scale of the additional entropy is is so small that we need not worry about its effects.

According to Marcus Huber at the Austrian Academy of Sciences in Vienna, who was part of the research team, the increase in entropy from timekeeping may be related to the “arrow of time”. It has been suggested that the reason that time only flows forward, and not in reverse, is that the total amount of entropy in the universe is constantly increasing, creating disorder that cannot be put in order again.

The relationship found by the researchers is a limit on the accuracy of a clock; it is not the case that a clock which creates the most possible entropy is the most accurate. Thus, a large and inefficient grandfather clock isn’t more precise than an atomic clock. Huber puts it like this, “It’s a bit like fuel use in a car. Just because I’m using more fuel doesn’t mean that I’m going further or faster”.

Interestingly, when the researchers compared their results with theoretical models developed for clocks that rely on quantum effects, they were surprised to find that the relationship between accuracy and entropy seemed to be the same for both. Ares thinks that this is hinting at the universality of thermodynamic laws as they apply to clocks. We cannot yet be sure if these results are universal, because there are many types of clocks for which the relationship between accuracy and entropy haven’t been tested, and this includes real devices such as atomic clocks, which push the ultimate quantum limits of accuracy.

Understanding the relationship discovered by Ares and the research team could be helpful for designing clocks in the future, especially those used in quantum computers and other devices where both accuracy and temperature are vital. It could also further our understanding of the quantum world more generally as to how the quantum and classical worlds are similar and different in terms of thermodynamics and the passage of time.

Just how the newly discovered linear relationship between increased timekeeping accuracy in clocks and increased entropy might affect devices for personal timekeeping is yet to be seen, but it may be a matter of “when” rather than “if”. In the same issue of New Scientist in which I found Leah Crane’s article, is another article of potential interest in the field small-scale devices such as watches and phones. In “IBM’s new climate-friendly chip”, by Matthew Sparkes, we are introduced to the world’s first 2-nanometre chip which could use 75% less energy than those in use today. The working prototype contains transistors that are 12 nanometres wide, which is just 24 silicon atoms across, and IBM is planning to go into production with these chips in late 2024. According to IBM, the 2-nanometre chips can be used in everything from phones and tablets to very high-performance server chips and supercomputers - the decreased size of the transistors offers the potential of smaller, faster and more efficient chips.



Particular acknowledgment to “The cost of keeping time” by Leah Crane, in New Scientist, 15 May 2021.

The main article for this research is at Physical Review X, “Measuring the Thermodynamic Cost of Timekeeping” published on 6 May 2021 and authored by A. N. Pearson, Y. Guryanova, P. Erker, E. A. Laird, G. A. D. Briggs, M. Huber and N. Ares. It is available as PDF download.

Another synopsis of this story appears in Physics 14, s54 as “Keeping Time on Entropy’s Dime”, online at physics.aps.org/articles/v14/s54 There is a link on this site back to the main journal article cited here above.

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