{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T12:05:28Z","timestamp":1785499528140,"version":"3.56.0"},"reference-count":21,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T00:00:00Z","timestamp":1781568000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006595","name":"UEFISCDI","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006595","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100006595","name":"National University of Science and Technology POLITEHNICA Bucharest","doi-asserted-by":"publisher","award":["PN-IV-P7-7.1-PTE-2024-0505"],"award-info":[{"award-number":["PN-IV-P7-7.1-PTE-2024-0505"]}],"id":[{"id":"10.13039\/501100006595","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006595","name":"National University of Science and Technology POLITEHNICA Bucharest","doi-asserted-by":"publisher","award":["34808\/19.09.2025"],"award-info":[{"award-number":["34808\/19.09.2025"]}],"id":[{"id":"10.13039\/501100006595","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Shannon entropy is the most common measure that one could use to check if a data source has random behaviour or not. A value close to the maximum is usually considered as evidence that the source is \u201crandom enough\u201d. The present paper shows that this criterion alone is not enough. A deterministic logistic map driven at r=3.9999 reaches 94.97% of the Shannon maximum, yet it is fully predictable once we look at the built-in patterns: its permutation entropy drops to 77.01% of the maximum and its sample entropy falls to 0.67, against 2.33 for a high-quality pseudo-random generator (PRNG). Building on this observation, we combine four entropy measures\u2014Shannon, R\u00e9nyi, permutation, and sample\u2014into a single diagnostic profile of the analyzed source. In order to validate our approach with practical, real life data, we test it on 2538 official draws of the Romanian Loto 6\/49 lottery, recorded between August 1993 and April 2026. The lottery historical data set is very close to a high-quality PRNG (pseudo-random number generator) from the point of view of all four measures. We also observe that the entropy deficit of both the lottery and the PRNG decays as a power law with exponent \u03b1\u2248\u22120.96; in contrast, the logistic map sits at \u03b1\u2248\u22120.07. A Random Forest classifier trained only on the entropy profile reaches 78% accuracy on the analyzed four-way classification task (lottery, PRNG, logistic map, biased distribution), but scores 55.7% on the binary lottery-versus-PRNG task, consistent with chance. The method introduced in this study is domain-independent and applies directly to RNG certification, cryptographic key auditing, and any setting where structured pseudo-randomness has to be ruled out.<\/jats:p>","DOI":"10.3390\/e28060695","type":"journal-article","created":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T05:56:31Z","timestamp":1781675791000},"page":"695","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Shannon Entropy and Beyond: An Information-Theoretic Framework for Randomness Pre-Screening"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-7014-2196","authenticated-orcid":false,"given":"Alexandru","family":"Dinu","sequence":"first","affiliation":[{"name":"Faculty of Electronics, Telecommunications and Information Technology, National University of Science and Technology POLITEHNICA Bucharest, 061071 Bucharest, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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