# What is the smallest entropy value ever measured?

Entropy is measured in J/K or in J/K/mol. What is the smallest value ever measured in an experiment? Google Scholar does not seem to help.

In other words, how good are scientists at measuring small entropy values?

EDIT: I found this paper containing some quite small measured entropy values at low temperature, in Table 8: D. R. Smith and F. Fickett, Low-temperature properties of silver, Journal of Research of the National Institute of Standards and Technology volume 100, page 119 (1995).

EDIT2: The answer below refers to a measurement that gave around 1000 k.

Can quantized transport experiments at ow temperature yield smaller values?

• Entropy cannot be measured directly. It would be calculated by measuring a heat flow and dividing by the temperature. But in any case entropy, like most thermodynamic properties, is an emergent property of large systems. For example an isolated electron does not have an entropy so it could not be measured even in principle. So it is not obvious what measuring a small entropy would mean since it isn't defined for small systems. Commented Jan 18, 2023 at 6:01
• The lowest entropy value (closest to zero) ever measured or inferred is probably related to superfluid helium, or other cold systems very close to absolute zero. I've heard of systems consisting of on the order of 10 atoms, whose log(possible configurations) is probably single digits. Commented Jan 18, 2023 at 7:14
• In this related answer I put in my two bits (pun intended). A serious answer might address the low entropy content of superfluids and/or the quark-gluon plasma. Note that entropy is an extensive quantity, so it might be more interesting to ask about low specific entropy, which might have units like joules per (kelvin $\cdot$ mole).
– rob
Commented Jan 18, 2023 at 7:16
• Possibly related: What is the simplest reason why an "entropometer" cannot exist? Commented Jan 18, 2023 at 10:33
• @RC_23 Do you have a paper at hand? Commented Jan 19, 2023 at 20:43

## 1 Answer

Olf et. al. Nature Physics 2015 (arxiv version) generate a very low entropy Bose-Einstein condensate (BEC) of Rb atoms. They claim an entropy of $$S/N = 0.001\text{ } k_B$$ where $$S$$ is the total entropy and $$N$$ is the number of particles in the BEC. It seems $$N \approx 10^6$$.

This was back in 2015. At the time I remember conversations about "is this the lowest entropy ever acheived" but I wasn't really involved so I don't remember the details. Likely lower entropies have been realized and measured in the field of ultracold atomic physics. Likely in Fermi quantum gas microscopes which rely on very low entropy to realize novel quantum phases. You may be able to get your answer by researching review articles on quantum gas microscopes and things like anti-ferromagnetism in quantum gas microscopes.

There may be physical systems with lower entropy than ultracold atomic ensembles but I'm not personally aware of them.

• Thank you. That would yield around 1000k as the entropy value. It will be interesting to see whether this will be beaten. One candidate are the quantized conduction experiments. But they are not my speciality... Commented Jan 29, 2023 at 7:45