Thanks a lot to Gianmichele Blasi and Géraldine Haack from Uni Geneva, Yuri Minoguchi and @entangledanarchist.bsky.social from Vienna for the amazing collaboration where we combined tools from quantum transport, condensed matter and thermodynamics to arrive at this cool result!

This phenomenon is rooted in the spectral rigidity also encountered in random matrix theory, and ubiquitous in fermionic systems. Thus, rigidity of the resulting time signal in this clock is remarkably robust: thermal noise, disorder, and finite size effects only perturbatively affect the scaling.

Therefore, when two excitations (ticks) are too close to each other, the following excitation arrives a bit later, correcting for the previous error. This leads to an exponentially reduced variance growth compared to independent errors.

For independent errors, the timing variance usually grows linearly in time. Here, the fermionic excitations are intrinsically correlated due to the Pauli statistics. This prevents excitations from clustering too closely together but also from being too far apart.

time-reversal with indefinite causal order

sounds fishy 🐟

In that sense, I'd put thermo on a level above, a meta-theory.

Good question! Well, I think it would indeed be more appropriate to put thermo on a different level of the hierarchy. Thermo is based on very general principles and those are usually fulfilled by microscopic theories which is why we see emergent thermodynamic phenomena in QTFs or also GR.

Thanks and congrats of course too 😀 Will be a volume with exciting theory

The beautiful artistic illustration in the first post is by Alexander Rommel (www.aerroscape.de), copyright by Alexander Rommel / TU Wien. I also thank my fantastic collaborators from @tuwien.at, @iqoqi-vienna.bsky.social, Chalmers and Malta from the @aspects-quantum.bsky.social consortium!

What this project also shows in my opinion is how important it is to create an informal, inviting and friendly discussion culture in science where also junior people happily express their opinions and thoughts; and how such an environment can seed exciting scientific projects. go.nature.com/4jWxUm7

Here, you can see an animation of the excitation travelling around a ring of 50 sites (y-axis = occupation probability, x-axis = where).

For example with quantum clocks it is possible to circumvent such limitations. The ring-clock does this by counting cycles completed by a single quantum particle traveling a ring. Since coherent transport is dissipation-free, this clock breaks the linear entropy-precision bound exponentially.

Generally, the more accurate a clock is, the more entropy it produces. For a wide range of classical stochastic clocks this is proved by the so-called "Thermodynamic Uncertainty Relation", which provides a linear relationship between clock precision and entropy.

Fantastic, congrats!