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Spectral measurements acquired below and above the lasing threshold, under varying magnetic fields, are statistically analyzed. Shannon entropy analysis reveals that the intensity fluctuations of each random laser mode, which show the emergence of random laser emission peaks, result in low entropy values. We find a positive correlation between Shannon entropy and the stability index  of the L\u00e9vy distribution of output intensities for all magnetic fields and pump energies investigated. As an application, we implement a machine learning approach to classify and predict the magnetic field and pump energy from individual spectra when that information is not available. When the network receives only the spectra as input, the prediction accuracy of the model reaches 69%, but when Shannon entropy is also included as an additional feature, the accuracy increases to 98%. These results demonstrate that Shannon entropy provides relevant complementary information for both the physical characterization of random laser dynamics and the development of efficient real\u2010time optical sensing systems.<\/jats:p>","DOI":"10.1002\/nap2.70234","type":"journal-article","created":{"date-parts":[[2026,8,8]],"date-time":"2026-08-08T03:37:32Z","timestamp":1786160252000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Shannon Entropy and L\u00e9vy Statistics for Machine Learning\u2010Assisted Spectral Sensing in Random Fiber Lasers With Magnetic Core\u2013Shell Nanoscatterers"],"prefix":"10.1002","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0548-668X","authenticated-orcid":false,"given":"Emanuel P.","family":"Santos","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica Universidade Federal de Pernambuco  Recife Pernambuco Brazil"},{"name":"Universidade Estadual de Alagoas\u2014Campus VI  Macei\u00f3 Alagoas Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenyu","family":"Du","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Opto\u2010Electronic Information Acquisition and Protection Technology Information Materials and Intelligent Sensing Laboratory of Anhui Province Key Laboratory of Opto\u2010Electronic Information Acquisition and Manipulation of Ministry of Education School of Physics and Opto\u2010electronics Engineering Anhui University  Hefei China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2831-6878","authenticated-orcid":false,"given":"Edwin D.","family":"Coronel","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Universidade Federal de Pernambuco  Recife Pernambuco Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alyson J. A.","family":"Carvalho","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Universidade Federal de Pernambuco  Recife Pernambuco Brazil"},{"name":"Centro de Ci\u00eancias e Tecnologia Universidade Estadual da Para\u00edba  Campina Grande Para\u00edba Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2609-9400","authenticated-orcid":false,"given":"G.","family":"Palacios","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Universidade Federal de Pernambuco  Recife Pernambuco Brazil"},{"name":"Centro de Ci\u00eancias Exatas e Sociais Aplicadas Universidade Estadual da Para\u00edba  Patos Para\u00edba Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5882-2670","authenticated-orcid":false,"given":"Cec\u00edlia L. A. V.","family":"Campos","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Universidade Federal de Pernambuco  Recife Pernambuco Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-7417-1301","authenticated-orcid":false,"given":"Zhijia","family":"Hu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Opto\u2010Electronic Information Acquisition and Protection Technology Information Materials and Intelligent Sensing Laboratory of Anhui Province Key Laboratory of Opto\u2010Electronic Information Acquisition and Manipulation of Ministry of Education School of Physics and Opto\u2010electronics Engineering Anhui University  Hefei China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4178-8266","authenticated-orcid":false,"given":"Ernesto P.","family":"Raposo","sequence":"additional","affiliation":[{"name":"Laborat\u00f3rio de F\u00edsica Te\u00f3rica e Computacional Departamento de F\u00edsica Universidade Federal de Pernambuco  Recife Pernambuco Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6536-6570","authenticated-orcid":false,"given":"Anderson S. 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