Has the entropy of a single photon been measured?

Question

From https://physics.stackexchange.com/questions/749311/has-the-entropy-of-a-single-photon-ever-been-measured

The entropy of single photons is some factor of order unity times the Boltzmann constant. The quantity has been discussed in many theoretical papers. Some are mentioned below.

The photon is assumed to have a known (not fully specified) energy, and no known polarization.

Have measurements of the single-photon entropy ever been performed or published? Google Scholar yields nothing on the issue. The question is thus: has the entropy of a single photon taken out from a photon field ever been measured?

Or is there some other experimental confirmation of single-photon entropy?

Here are some theoretical references:

Li, Li and Yang, 2022 https://www.mdpi.com/1099-4300/24/11/1609#FD2-entropy-24-01609

van Enk, S.; Nienhuis, G. Entropy production and kinetic effects of light. Phys. Rev. A 1992, 46, 1438–1448.

Kirwan, A.D. Intrinsic photon entropy? The darkside of light. Int. J. Eng. Sci. 2004, 42, 725–734.

Zimmermann, H. Particle Entropies and Entropy Quanta II. The Photon Gas. Zeitschrift für Physikalische Chemie 2000, 214, 347.

Comments

I think many relevant comments have already been made on the other site.

Entropy, just like temperature, is a quantity characterising an ensemble. These quantities are not defined for a single photon. While it may make sense to consider an average contribution of a photon to the entropy of a photon gas, I do not see how a definitive entropy (or temperature) should be assigned to a single photon. If you choose not to measure all measurable quantities of a single photon, you remain ignorant about some of these quantities, but this ignorance does not bestow entropy on the photon.

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@Flamma; A photon can be in a mixed state corresponding to a canonical ensemble. Thus if one attributes mixed states to single pquantum systems then single photons also may have temperature and entropy. But if one attributes mixed states only to ensembles of systems then a single photon has no well-defined temperature or entropy.

Thus the answer depends on the interpretation of quantum mechanics.

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A single photon may have some energy, not a temperature. High-energy detectors of single photons measure the energy with their calorimeters ;-)