Breaking Thermodynamic Limits: The Future of Timekeeping

A new study reveals that the accuracy of quantum effects¹ is better than expected. This study comes as researchers from TU Wien and collaborators make use of quantum metrology for the atomic clock.

An atomic clock uses the quantum properties of atoms to measure time far more accurately than conventional clocks. These most precise timekeepers of the world are known for their unprecedented accuracy by using lasers to measure the vibrations of atoms, which oscillate at a constant frequency.

But when it comes to the fundamental laws of quantum physics, there’s always some uncertainty, so a certain amount of statistical noise is to be expected and needs to be accepted. This noise or randomness puts a limit on the accuracy achieved. 

So, atomic clocks could be even more precise, and if they can measure atomic vibrations more accurately, they would be sensitive enough to identify phenomena such as dark matter and help answer questions like what effect gravity might have on the passage of time.

Interestingly, it is believed that for an atomic clock to be more accurate, it needs more energy to achieve that precision. 

Back in 2021, an experiment² reported a limit to the accuracy of clocks with nature imposing a fundamental energy cost for keeping time. Per the research, clocks that measure time more accurately consume more energy than their less accurate counterparts. 

With a key principle of thermodynamics being that energy always flows from hot objects to cold ones, reversing this flow (like in a refrigerator) means we have to pay for it elsewhere.

So, a clock requiring at least twice as much energy to be twice as accurate seems to be an immutable law, that is, until now.

A team of scientists from TU Wien, the University of Malta, and Chalmers University of Technology has shown that by using special tricks, we can increase accuracy exponentially. 

The key point here is in using two different time scales, much like how a standard clock has a minute hand and a second hand.

How Quantum Physics is Redefining the Entropy Cost of Time

Physical devices that operate out of equilibrium are influenced by thermal fluctuations (random deviations of a system from its average state), which limit the accuracy of their operation. This problem is more noticeable at tiny and quantum scales, where we need entropy dissipation to mitigate it.

In the case of clocks, a thermodynamic flux towards equilibrium is required to measure time, resulting in a minimum entropy dissipation per tick. 

Although both classical and quantum models tend to show a linear association between precision and dissipation, the relationship is still not so clear. 

In the quest for the most accurate atomic-based clocks, which could possibly transition to nuclear power in the future, these costs are not the most pressing concern, but for small,  self-contained quantum control, the exact relationship between dissipation and precision is potentially a practical concern. 

With that in mind, the researchers have now presented an autonomous quantum clock model that has achieved accuracy that scales exponentially with the dissipation of entropy. 

This achievement is enabled by coherent transport in a spin chain with customized couplings, where entropy dissipation is restricted to a single link, said the study. The results show that coherent quantum dynamics can exceed the precision limits of traditional thermodynamics, potentially helping the development of future low-dissipation, high-precision quantum devices.

“We have analyzed in principle, which clocks could be theoretically possible.”

– Professor Marcus Huber from the Atomic Institute at the TU Wien

He explained that there are two components that a clock needs. The first one is a time-based generator, like a quantum oscillation or a pendulum. The second one is a counter, which is an element that counts the time units, as defined by the time base generator, that have passed.

The time base generator always returns to exactly the same state, or the pendulum is exactly where it was before completing one oscillation. 

Meanwhile, in an atomic clock, the caesium atom returns to the very same state it was in before, after a certain number of oscillations. The counter, however, must change for a clock to be useful.

“This means that every clock must be connected to an irreversible process. In the language of thermodynamics, this means that every clock increases the entropy in the universe; otherwise, it is not a clock.” 

– Florian Meier from TU Wien

In a pendulum clock, the pendulum generates some heat and disorder among the air molecules around it. In the case of an atomic clock, every laser beam that reads the state of the clock generates heat as well as radiation and thus entropy. According to Marcus Huber:

“We can now consider how much entropy a hypothetical clock with extremely high precision would have to generate – and, accordingly, how much energy such a clock would need. Until now, there seemed to be a linear relationship: if you want a thousand times the precision, you have to generate at least a thousand times as much entropy and expend a thousand times as much energy.”

But the team from TU Wien, in collaboration with researchers from the University of Malta, Chalmers University of Technology, and the Austrian Academy of Sciences (ÖAW) has now demonstrated that this so-called rule can be evaded by using two different time scales.

For instance, as Meier shared, particles that move from one area to another can be used to measure time, much like how sand grains do by falling from the top of the glass to the bottom.

A series of such time-measuring devices can be connected in series, and then you can count just how many of them have already passed through. This would be similar to how the bigger clock hand counts the number of laps the smaller clock hand has already completed.

“This way, you can increase accuracy, but not without investing more energy,“ said Marcus Huber. “Because every time one clock hand completes a full rotation and the other clock hand is measured at a new location – you could also say every time the environment around it notices that this hand has moved to a new location – the entropy increases. This counting process is irreversible.”

Yet another kind of particle transport allowed by quantum physics is traveling through the entire structure. Here, particles travel across the dial of the clock without being measured.

During this process, the particle, in a way, is everywhere with no clearly defined location until it actually arrives at last. It is then that the particle is measured, in a process that’s irreversible and increases entropy.

So, the team has two processes: a fast one that doesn’t result in entropy or quantum transport, and the other one where the particles arrive at the very end.

“The crucial thing about our method is that one hand behaves purely in terms of quantum physics, and only the other, slower hand actually has an entropy-generating effect.”

– Yuri Minoguchi of TU Wien

The team has demonstrated that the strategy allows for a significant increase in precision with every increase in entropy, so higher precision than previously thought possible can be achieved.

“What's more, the theory could be tested in the real world using superconducting circuits, one of the most advanced quantum technologies currently available.”

– Study co-author Simone Gasparinetti, who’s a leader of the experimental team at Chalmers 

Huber called this a crucial outcome for research into highly accurate quantum measurements as well as suppressing unwanted fluctuations. Moreover, the research, Huber noted, “helps us to better understand one of the great mysteries of physics: the connection between quantum physics and thermodynamics.”

Click here to learn how thorium is powering ultra-precise nuclear clocks.

The Future Impact of Quantum Timekeeping on Humanity

One of the most precious resources for us humans is time, which is limited and irreversible. Time is fundamental to our existence and progress.

To keep track of our time, people developed calendars, and then as societies got more complex and technological in nature, it became more important to have accurate timekeeping. 

What timekeeping needs is something that oscillates with a steady beat and another something that counts those beats as well as displays the time. 

This led to the development of clocks, which got sophisticated over time with pendulums and quartz oscillators. 

From wristwatches to clocks used on satellites, most modern clocks still keep time using a quartz crystal oscillator. When a voltage is applied to the oscillator, it vibrates at a precise frequency, which acts like the pendulum in a pendulum clock, ticking off the time passed.

But the problem was that no two clocks were the same. And with the world becoming more integrated, there was a need for a consistent and accurate way to measure time. An atomic clock was a natural solution.

The dream of the atomic clock actually started more than a century ago when scientists James Maxwell and William Thompson proposed the idea. 

Atoms are the basic building blocks of all matter. At the core of atoms is the nucleus, which consists of protons and neutrons, surrounded by electrons, which can vary in number. Electrons are arranged in distinct energy levels, traveling in circular orbits around the nucleus. 

With atoms absorbing and emitting light waves of specific frequencies, scientists reasoned that atoms of a specific element are identical to one another and never change, so the frequencies of light they absorb and emit shouldn’t either. 

While the idea first came into existence in the late 19th century, it was not until much later that an atomic clock was actually developed. 

As it happens, war tends to serve as a powerful catalyst for scientific and technological advancements. It was war that led to inventions like the microwave oven, GPS, computers, and more, which today have profound effects on our daily lives. 

The atomic clock also came at such a time. In 1939, physicist Isidor Rabi proposed that scientists at the National Institute of Standards and Technology (NIST) (the National Bureau of Standards (NBS) at the time) use the newly developed molecular beam magnetic resonance technique that provided precise measurements of nuclear magnetic moments as a time standard. 

He then measured the frequency at which cesium atoms naturally absorb and emit microwaves, which was around 9.1914 billion cycles per second, and talked about it years later, which was described by the NYT as a “cosmic pendulum” tapping into “radio frequencies in the hearts of atoms.”

A clock based on ammonia was demonstrated in 1949, but it ultimately proved no more accurate than existing ones.

Over time, new technological innovations like optical pumping; which created much stronger magnetic resonance and microwave absorption signals, and Ramsey interferometry; which was for molecular beam spectroscopy, led to advances in the field and prompted other scientific groups to study the same.

By 1975, the atomic clock from NIST was accurate enough to neither gain nor lose a second in 400,000 years, while in 1993, their atomic clock became even more accurate, not gaining or losing a second in 6 million years. 

In 2019, NASA developed the Deep Space Atomic Clock to help make spacecraft navigation to distant locations like other planets more autonomous. This one will be off by less than a nanosecond after four days and less than a microsecond after a decade, which is equivalent to being off by only one second every 10 million years.

NASA’s atomic clock was about 50 times more stable than its counterparts on GPS satellites, and this was achieved with the help of mercury atoms. 

The “precise and stable value” of the energy difference between orbits “is really the key ingredient for atomic clocks,” said Eric Burt, an atomic clock physicist at Jet Propulsion Laboratory (JPL) at the time. “It’s the reason atomic clocks can reach a performance level beyond mechanical clocks.”

The kind of precise timekeeping that atomic clocks produce is not required for day-to-day life, but it has profound implications in many other industries. Atomic clocks have actually led to advances in metrology, communication, advanced navigation systems, and satellite-based positioning.

Now, the knowledge gained through the latest research aims to spur many more advances. It is expected to be extremely beneficial across sectors, including artificial intelligence (AI), robotics, and other emerging fields.

For instance, by powering advanced gravitational wave detectors and climate monitoring satellites, quantum clocks can boost the detection of subtle Earth system signals. They further provide more precise time references that can enable new levels of measurement for sea level rise, tectonic shifts, and underground mapping.

In the world of AI, meanwhile, models that combine data with distributed sensors for smart factories, precision farming, or financial trading can benefit from accurate atomic clocks. It can also help with quantum-enhanced AI hardware, where quantum timekeeping can stabilize error-prone quantum processors used for machine learning. Reliable qubit control, after all, depends on precise timing and phase coherence.

From autonomous vehicles to drones and robots, they all rely on GPS navigation and local clocks. So, highly accurate quantum clocks here can enable ‘GPS-denied’ navigation. They can also help robot swarms to coordinate better for complex tasks like distributed mapping and search-and-rescue.

Communications is another field that can benefit a lot from these clocks in terms of range and stability. Future wireless and photonic networks will also benefit as they require ultra-precise timing for low-latency edge computing and device handovers.

Investing in the Advanced Measurement Industry

Honeywell International (HON +0.21%) is a leader in advanced measurement systems, including highly precise timing devices, atomic clock technologies for aerospace and defense, and even quantum computing through Quantinuum, formed by the merger of Cambridge Quantum and Honeywell. 

The company primarily operates through:

Aerospace Technologies

• Supplies products, software, and services for aircraft.
• Serves equipment manufacturers, air transport, and aviation sectors.

Industrial Automation

• Provides automation solutions for intelligent, sustainable, and secure operations.
• Targets industries such as petrochemicals and life sciences.

Building Automation

• Delivers solutions to ensure safe and sustainable facilities.

Energy and Sustainability Solutions

• Offers licensing capabilities integrated with material science and chemistry.

Honeywell International (HON +0.21%)

Honeywell has a market cap of $154.5 billion with its shares currently trading at fresh highs at $241, up 6.4% YTD. It has an EPS (TTM) of 8.70 and a P/E (TTM) of 27.62, while the dividend yield offered is 1.88%.

For Q1 2025, the company reported sales of $9.8 billion and earnings per share of $2.22. During this period, Honeywell used $2.9 billion for share repurchases, dividends, and capital expenditures.

“Honeywell started the year off exceptionally well, exceeding guidance across all metrics, led by solid organic growth. For the third straight quarter, we delivered both sequential and year-over-year backlog growth, driven by healthy order rates and continuing customer demand for our differentiated offerings.”

– CEO Vimal Kapur

Conclusion

Quantum-enhanced timekeeping shows that with continued experiments, even the most fundamental limits in physics can be rethought. With the latest research, as our understanding of quantum thermodynamics advances, so will our ability to measure time with great precision. 

By combining clever architectures and deep knowledge of entropy, researchers are challenging old assumptions about energy and entropy costs and paving the way for a new era of hyper-accurate systems with far-reaching impacts on technology, infrastructure, science, and the universe.

Studies Referenced:

1. Meier, F.; Minoguchi, Y.; Sundelin, S.; Bernhardt, N.; Särkkä, J.; Bohrdt, A.; Gring, M.; Demler, E.; Schmiedmayer, J. Precision is Not Limited by the Second Law of Thermodynamics. Nat. Phys. 2025, Advance online publication. https://doi.org/10.1038/s41567-025-02929-2
2. Pearson, A. N.; Guryanova, Y.; Erker, P.; Laird, E. A.; Briggs, G. A. D.; Huber, M.; Ares, N. Measuring the Thermodynamic Cost of Timekeeping. Phys. Rev. X 2021, 11 (2), 021029. https://doi.org/10.1103/PhysRevX.11.021029