heading towards entropy tick-by-tick

Disorder may be most familiar from one’s messy desk. And it is not alone in the Universe. Since the Big Bang 13 billion years ago, entropy is steadily increasing. This is the main statement of the second law of thermodynamics. If one considers the Universe as a closed system, then entropy can only in-, but never decrease. According to thermodynamics, it would thus one day reach its theoretical maximum which would mean the complete absence of any ordered structures.

An international team headed by Marcus Huber from the IQOQI Vienna was now able to show, using a Gedankenexperiment, that every tick of a clock not only measures the passing of time (and with it the increase of entropy), but indeed increases the entropy by ticking itself. The researchers report their findings in the journal Physical Review X. In an interview, Marcus Huber explains why clocks create entropy and why we can’t measure time with infinite precision.

Usually quantum theory does not care much about the nature of time. How did you come up with this particular Gedankenexperiment?

Marcus Huber: Because time is one of the strangest mysteries in quantum physics. In quantum, but also classical, mechanics there is no reference to a direction of time. Let’s imagine a movie of two billiard balls that scatter in a perfect way. Is this movie played forward or backward? It is impossible to tell. The same is true for elementary quantum particles. Now if all fundamental laws are invariant to switching the directionality of time, why do we remember the past, why do our clocks run forward?

Why did you come up with the concept of autonomous quantum clocks to investigate this question?

Huber: To say something scientific about time we have to measure it, i.e. we have to build clocks. The most accurate clocks today are also essentially quantum mechanical, such as atomic clocks that operate on similar principles. Our team was asking the question: If we were able to build the most perfect clock, constrained only by the laws of quantum mechanics, how accurate could it be? For that we had to break down the process of measuring time into its elementary constituents. The smallest clock that is compatible with the laws of quantum mechanics consists of at least two, or in case of autonomous clocks three, quantum systems. Autonomous in this context means that the clock and all of its resources are self-contained and its operation does not require another clock operating in the background.

Even a clock contributes to entropy. The more accurate it ticks, the more entropy it has to dissipate per tick. Every tick has a fundamental entropy cost.

The whole concept presently only exists as a computer simulation. How can one imagine a “perfect clock” concretely?

Huber: Our thought experiment shows that clocks are essentially machines that harness a tendency of out-of-equilibrium resources to tend to equilibrium. They use this process to produce measurable “ticks”. In our mathematical model used in the computer simulation, our clock operates using two thermal reservoirs at different temperatures coupled to a two-qubit machine. This induces a heat flow from the hot reservoir to the cold one which in turn powers the clock. We are also planning to build such a clock, with slight modifications, in the lab, it is by no means science fiction. But this is a situation where an experiment is not adding any additional insight. It is about the theoretical principle, thinking about the “clock of clocks”, the best clock that could be built based only on the laws of quantum mechanics.

You then turned your investigation to the laws of thermodynamics.

Huber: One of the most intuitive explanations for an arrow of time, i.e. the separation of events into past and future, is the second law of thermodynamics. To return to our movie example: If I see a coffee cup smashing on the floor, it is easy to tell whether the movie runs backwards or forwards. The process is not reversible. Colloquially speaking “the disorder” is steadily increasing. What our thought experiment shows: Even a clock contributes, the more accurate it ticks, the more entropy it has to dissipate per tick. Every tick has a fundamental entropy cost.

Does this mean that there is also in quantum mechanics no perpetuum mobile?

Huber: Yes, or with other words: Clocks are also only machines. You would want clocks to have two properties: Accuracy and resolution, i.e. the time-scale relative to other clocks. Both figures of merit are competing. To build an accurate clock I need a lot of energy/entropy, unless I scale down the resolution (i.e. the frequency of ticks) and thereby reduce the cost again. One could even imagine a clock running at 100% efficiency, i.e. virtually not using up any entropy/energy in its operation, but such a clock could never tick.

One could even imagine a clock running at 100% efficiency, i.e. virtually not using up any entropy/energy in its operation, but such a clock could never tick.

Do your results have consequences for our understanding of time?

Huber: Our every-day understanding will not be touched, but it is interesting in the context of quantum mechanics. There, time appears as a classical parameter, i.e. we pretend that in theory it is measurable with arbitrary precision. But our research shows that there are limits. We can maximize accuracy, by scaling up the energetic resources, but those resources are finite. And with a finite amount of energy available we can only build finitely accurate clocks. We have to come to terms with the fact that within quantum mechanics, time is not measurable to arbitrary precision.

Could one say: The more accurately we measure time, the faster we are approaching the end of time itself?

Huber: Yes, every tick uses resources in an irreversible way.

Wouldn’t it be better if you built fewer clocks then?

Huber: Clocks are the least of my worries. We are talking about quantum mechanical units of energy, even if I were to build a million perfect quantum clocks, I would not reach the energy use of a light bulb. I think we can continue researching in this direction.