# 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. Jan 18 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. Jan 18 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
Jan 18 at 7:16
• Possibly related: What is the simplest reason why an "entropometer" cannot exist? Jan 18 at 10:33
• @RC_23 Do you have a paper at hand? Jan 19 at 20:43

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 $$N \approx 10^6$$.