# Has the entropy of a single photon ever been measured?

Light fields have entropy, as already discussed by Planck. As a consequence, photons have entropy.

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

For the present question, 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?

EDIT 1 and 2 combined: 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.

• Can you be a bit more specific on your sources? The only thing I can find at first glance is a recent paper from a dubious publisher and even that appears to be focussing on photon gases. Apart from that, neither is the entropy of a single photon a well defined thing (question on this) nor is entropy measurable directly measurable (questions on this: 1, 2). Feb 9 at 8:42
• I think it is worth expanding on what you mean by single photon entropy - the cited article gives multiple definitions. This way your question will be self-contained and interesting to the community. As now it is more of a reference request. Feb 9 at 14:21
• I agree with @RogerVadim and include your definition of what the allowable states of a photon are. Off the top of my head I count 3 states of polarization and 2 spin states. Feb 9 at 15:31

• This is totally true (pure state, zero entropy). However, you can define entropy for a "mixed state" or "probability density". Imagine having a single-photon detector that only emits a "bip" when detects a photon and you point it at a faint source that emits like a black body, and you know nothing else). This can be done whether or not you have a single particle or a million, you just apply $p \log p$. In this case, entropy measures your ignorance (if you know the exact pure state, your ignorance is 0: you know everything about the system). Feb 9 at 14:25
• @anna v The $\pm 1\hbar$ spin corresponds to right or left circularly polarized light. Feb 9 at 18:18