The most advanced clocks on the market today maintain an exact rhythm. However, a new experiment suggests that the precision of clocks comes at a cost: entropy.

Each time a clock ticks, entropy, or disorder, is created. Scientists have now quantified the entropy generated by a clock that can operate with varying degrees of precision. The more precise the clock’s ticks were, the more entropy was emitted, physicists report in a paper accepted for publication in Physical Review X.

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

Time and entropy are two concepts that are inextricably linked. Entropy is referred to as the “arrow of time” because it tends to increase over time — the universe appears to move inexorably from lower to higher entropy (SN: 7/10/15). This march toward increasing entropy explains why some processes can occur in the forward direction but not in the reverse direction: While it is simple to incorporate cream into coffee, it is exceedingly difficult to separate it again. Machines also contribute to disorder during operation, for example, by emitting heat, which increases the entropy of their surroundings. This means that even a simple battery-operated clock generates entropy as it ticks.
Physicists previously established a direct relationship between the maximum possible accuracy of their ticks and the amount of entropy emitted by tiny quantum clocks. However, larger clocks are far too complicated to perform such calculations. As a result, it was unclear whether such a rule applied to other types of clocks.

To determine the amount of entropy released during the ticking of a simplified clock, Ares and colleagues constructed one using a thin membrane suspended across two posts that were tens of nanometers thick and 1.5 millimetres long. The membrane flexed up and down in response to an electrical signal sent into the clock. This bending motion occurred at regular intervals, similar to the steady ticks of a clock, and was detected by an antenna. The greater the strength of the electrical signal, the more precisely the clock ticked. And as the accuracy of the clock improved, entropy — the amount of heat generated in the antenna’s circuit — increased in lockstep.

This finding implies that the theoretical relationship for quantum clocks holds for other types of clocks as well. “It’s nice to have that,” says Juan Parrondo, a physicist at Madrid’s Complutense University who was not involved in the study. “What I’m not certain of is the universality of the type of relationship they discover.” The researchers examined a single type of clock. According to Parrondo, it is unclear whether the relationship between accuracy and entropy holds for clocks in general.

However, some scientists believe the relationship is universal, illuminating a fundamental aspect of how clocks work. According to ETH Zurich quantum physicist Ralph Silva, the new study “would push us even further in this direction,” according to ETH Zurich quantum physicist Ralph Silva, who was not involved in the research. “It’s a data point in favour of the possibility that this is true for all clocks. However, this has not been established.”

To operate reliably, a clock must go through a process that has a preferred direction in time. If the clock did not generate entropy, it would run forward as well as backward equally likely. And the more entropy the clock generates, the less likely it will experience fluctuations — temporary backward steps that degrade the clock’s accuracy.

Therefore, if the accuracy of all clocks does come at the expense of increased entropy, this trade-off may reflect a close relationship between time and its measurement.

Journal Reference:

A. N. Pearson, Y. Guryanova, P. Erker, E. A. Laird, G. A. D. Briggs, M. Huber, and N. Ares Measuring the thermodynamic cost of timekeeping. Physical Review X. In press, 2021.

Main image Credit: Alex Berger, Flickr