{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T10:50:54Z","timestamp":1785408654386,"version":"3.56.0"},"reference-count":16,"publisher":"Optica Publishing Group","issue":"14","license":[{"start":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T00:00:00Z","timestamp":1783900800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T00:00:00Z","timestamp":1783900800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"crossref","award":["DP220101602"],"award-info":[{"award-number":["DP220101602"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/05mmh0f86","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Lett."],"published-print":{"date-parts":[[2026,7,15]]},"abstract":"<jats:p>\n                    A laser beam is often modelled by a pure coherent state. In fact, its state is mixed, even if it has coherent-state photon-number statistics (Poissonian), because the phase must vary. We consider such an ideal laser beam, with phase diffusion rate\n                    <jats:italic>\u2113<\/jats:italic>\n                    , equal to its (Lorentzian) spectral width. We show that the beam entropy is extensive, with an entropy flow of\n                    <jats:italic>S<\/jats:italic>\n                    \u02d9=\n                    <jats:italic>k<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>B<\/jats:italic>\n                    <\/jats:sub>\n                    <jats:italic>N<\/jats:italic>\n                    \u02d9\n                    <jats:italic>\u2113<\/jats:italic>\n                    , where\n                    <jats:italic>N<\/jats:italic>\n                    \u02d9 is the number flow. We give an intuitive explanation for this remarkably simple result and compare it to the entropy flow of a unidirectional thermal beam.\n                  <\/jats:p>","DOI":"10.1364\/ol.599036","type":"journal-article","created":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T18:00:11Z","timestamp":1782324011000},"page":"3977","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Entropy flow of a laser beam"],"prefix":"10.1364","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6815-854X","authenticated-orcid":true,"given":"Howard M.","family":"Wiseman","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02sc3r913","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,7,13]]},"reference":[{"key":"ol-51-14-3977-R1","doi-asserted-by":"publisher","first-page":"033001","DOI":"10.1088\/0031-8949\/91\/3\/033001","type":"journal-article","volume":"91","author":"Wiseman","year":"2016","journal-title":"Phys. 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All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}