Keeping time accurately comes with a price. The maximum accuracy of a clock is directly related to how much disorder, or entropy, it creates every time it ticks.

Natalia Ares at the University of Oxford and her colleagues made this discovery using a tiny clock with accuracy that can be controlled. The clock consisted of a 50-nanometre-thick membrane of silicon nitride, vibrated by an electric current. Each time the membrane moved up and down once and then returned to its original position, the researchers counted a tick, and the regularity of the spacing between the ticks represented the accuracy of the clock.

They found that as they increased the clock’s accuracy, the heat produced in the system grew, increasing the entropy of its surroundings by jostling nearby particles. “If a clock is more accurate, you are paying for it somehow,” says Ares.

In this case, you pay for it by pouring more ordered energy into the clock, which is then converted into entropy. “By measuring time, we are increasing the entropy of the universe,” says Ares. The more entropy there is in the universe, the closer it may be to its eventual demise. “Maybe we should stop measuring time.” The scale of the additional entropy is so small, though, that there’s no need to worry, she says.

The increase in entropy in timekeeping may be related to the “arrow of time”, says Marcus Huber at the Austrian Academy of Sciences in Vienna, who was part of the research team. It has been suggested that the reason that time only flows forward, 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.

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The relationship that the researchers found is a limit on the accuracy of a clock, so it doesn’t mean that a clock that creates the most possible entropy would be maximally accurate – hence a large, inefficient grandfather clock not being more precise than an atomic clock. “It’s a bit like fuel use in a car – just because I’m using more fuel doesn’t mean that I’m going faster or further,” says Huber.

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. “I think it’s hinting at this universality of how the laws of thermodynamics apply to clocks,” says Ares.

We can’t be sure yet that these results are actually universal, though, because there are many types of clocks for which the relationship between accuracy and entropy haven’t been tested. “It’s still unclear how this principle plays out in real devices such as atomic clocks, which push the ultimate quantum limits of accuracy,” says Mark Mitchison at Trinity College Dublin in Ireland.

Understanding this relationship could be helpful for designing clocks in the future, particularly those used in quantum computers and other devices where both accuracy and temperature are crucial, says Ares.

This finding could also help us understand more generally how the quantum world and the classical world are similar and different in terms of thermodynamics and the passage of time.

Journal reference: Physical Review X, DOI: 10.1103/PhysRevX.11.021029