Quanta Magazine

Paul Erker, a master's student in Physics, began to look through books and papers for the explanation of what a clock was. Albert Einstein once said that time is what a clock measures. Erker believed that a deeper understanding about clocks would lead to new insights into the nature of time.
He discovered that physicists didn't care much about the basics of timekeeping. They took time information as a given. Erker recently stated that I was not satisfied with the way clock literature dealt with clocks.

He began to think for himself about what a clock does and how it tells time. Some initial thoughts were his. In 2015, he went to Barcelona to complete his doctorate. Marcus Huber, a professor, was the leader of a group of physicists who took up Erkers' question. Huber, Erker, and their colleagues were experts in quantum information theory, quantum thermodynamics and other disciplines that deal with the flow of energy and information. These theoretical frameworks that underpin emerging technologies such as quantum computers and quantum engines provided the language to describe clocks.

Huber shared the idea that a clock was a thermal machine. Huber explained this over Zoom, his dark brown blond hair draped over a black T shirt. A clock uses energy to produce exhaust, much like an engine. Clocks use energy to tick, engines use it to propel.

The fundamental limits of timekeeping have been discovered by the researchers over the course of five years of research on the simplest clocks. They have discovered new relationships between accuracy and information, complexity, energy, and entropy, a quantity whose constant rise in the universe is closely related to the arrow of Time.

These relationships were only theoretical until Natalia Ares, an experimental physicist at Oxford, reported measurements of a tiny clock that strongly supports the new thermodynamic theory.

Nicole Yunger Halpern is a Harvard University quantum thermodynamicist who did not participate in the clock work. She believes the findings could be used to design autonomous, efficient quantum clocks that can control operations in future quantum computers.

This new view on clocks has provided fresh material for discussions about time. Yunger Halpern stated that this line of research does address fundamentally the role of time within quantum theory.

Gerard Milburn is a quantum theorist from the University of Queensland, Australia. He wrote a review paper about clock thermodynamics research last year.

What is a Clock?

First, it is important to remember that almost everything is a clock. Garbage signals the end of the day with its unpleasant odor. Wrinkles signify the passage of time. Huber, now at the Technical University of Vienna, and the Institute for Quantum Optics, Quantum Information Vienna, explained that you could measure the temperature of your coffee on your coffee table to determine the age.

Huber, Erker, and their colleagues in Barcelona realized early in their conversations that a clock was anything that undergoes irreversible change: changes in energy that spread out among more particles or a larger area. Entropy, which is a measure of energy's dissipation tends to rise because there are many more ways to spread it out than to keep it concentrated. This numerical asymmetry and the fact that energy was initially extremely concentrated at the beginning, is why energy moves towards more dispersed arrangements, one cool coffee cup at a. time.

Huber and Company claim that energy's strong spreading tendency, entropys resulting irreversible increase, and entropys account for times arrow. Huber stated that the irreversibility of energy is fundamental. This shift in perspective was what we wanted.

Coffee is not a great timekeeper. Like most irreversible processes it interacts with the air around it stochastically. To accurately estimate a time interval, you will need to calculate averaging over long periods of time. This includes many random collisions between air molecules and coffee molecules. We don't refer to coffee, garbage, or wrinkles as clocks.

That name was reserved by clock thermodynamicists for objects whose ability to keep time is increased by periodicity. It refers to any mechanism that space out the times when irreversible events occur. A good clock does more than just change. It ticks.

The clock will be more accurate if it is ticked more often. Erker, Huber, and co-authors published their first paper in Physical Review X 2017 and showed that accurate timekeeping has a price: the clock's accuracy is a function of its energy dissipation and how much entropy it generates in the course it ticks.

Milburn said that a clock is a flowmeter for entropy.

The ideal clock that ticks with perfect periodicity would consume infinite amounts of energy and produce infinite amount entropy. This is not possible. The accuracy of clocks is therefore fundamentally limited.

Erker and his colleagues examined the accuracy of the simplest clock that they could find: a system of three atoms. One atom is hot and connects to a heat source. A cold atom links to the environment. The third atom undergoes excitations and decays, so it's connected to all the other ticks. The heat source is the energy source that drives the ticks. Entropy occurs when the environment releases waste energy.

Researchers found that the frequency of the three-atom clock's ticks increases with increasing entropy. Huber explained that this relationship between clock accuracy, entropy, and frequency made intuitive sense, given the connection between information and entropy.

Entropy, in simple terms, is the measure of how many possible arrangements a system can have. Entropy increases as energy is distributed more evenly among particles. This is why energy disperses and entropy increases. In his 1948 paper, Claude Shannon, an American mathematician, demonstrated that entropy is also inversely related to information. The more information you have about a data set for example, the higher the entropy. This is because there are many possible states that the data could be in.

Huber stated that there is a deep connection between information and entropy. Therefore, any clocks limit on entropy production should correspond to a clocks limit of information. Huber also said that information about the past time would be helpful.

Theorists have expanded their three-atom clock model in a paper published in Physical Review X this year. They added complexity to the model by connecting more hot and cold atoms to the ticking atom. This complexity allows a clock to focus the likelihood of a tick occurring into smaller and narrower time windows, increasing its regularity and accuracy.

It is the irreversible increase in entropy which makes timekeeping possible. Both periodicity and complexity improve clock performance. It was not clear, however, how to verify teams equations or what simple quantum clocks, if any, had to do the ones on the walls.

Measuring ticks

Erker was seated next to Anna Pearson, an Oxford graduate student who had just given a talk that he found interesting at a conference dinner. Pearson was involved in studies on a vibrating membrane 50 nanometer thick. She made a casual comment that white noise, a random mixture of radio frequencies could stimulate the membrane. It vibrated because of the frequencies that resonated with it.

Erker described the noise as a heat source and the vibrations as ticks on a clock. Erker suggested that they collaborate.

Ares, Pearson's supervisor, was excited. Milburn had already suggested that the membrane could act as a clock. However, she hadn't heard of the new thermodynamic relationships developed by other theorists. This includes the fundamental limit to accuracy. We agreed that we could measure it! Ares stated. We can measure the entropy! We can also measure ticks

Although the vibrating membrane is not a quantum system it allows precise tracking of its movement and energy use. Ares stated that we can see how much the circuit's energy dissipation changes.

Her team and Erker set out to verify the 2017 paper's key prediction: that there should be a linear relationship of entropy production with accuracy. It wasn't clear if the relationship would hold for a more classical clock like the vibrating membrane. Huber stated that when data began to roll in, the first plots were revealed and we realized there was a linear relationship.

Regularity of membrane clocks vibrations was directly related to how much energy was entered into the system and how many entropy it generated. These findings suggest that the thermodynamic equations that theorists developed may be universally applicable to timekeeping devices.