{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T22:14:50Z","timestamp":1780524890591,"version":"3.54.1"},"reference-count":42,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T00:00:00Z","timestamp":1737504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>I study a lattice with periodic boundary conditions using a non-local master equation that evolves over time. I investigate different system regimes using classical theories like Fisher information, Shannon entropy, complexity, and the Cram\u00e9r\u2013Rao bound. To simulate spatial continuity, I employ a large number of sites in the ring and compare the results with continuous spatial systems like the Telegrapher\u2019s equations. The Fisher information revealed a power-law decay of t\u2212\u03bd, with \u03bd=2 for short times and \u03bd=1 for long times, across all jump models. Similar power-law trends were also observed for complexity and the Fisher information related to Shannon entropy over time. Furthermore, I analyze toy models with only two ring sites to understand the behavior of the Fisher information and Shannon entropy. As expected, a ring with a small number of sites quickly converges to a uniform distribution for long times. I also examine the Shannon entropy for short and long times.<\/jats:p>","DOI":"10.3390\/e27020105","type":"journal-article","created":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T05:50:53Z","timestamp":1737525053000},"page":"105","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Hyperbolic Diffusion Functionals on a Ring with Finite Velocity"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4551-6161","authenticated-orcid":false,"given":"Marco","family":"Nizama","sequence":"first","affiliation":[{"name":"Departamento de Fisica, Facultad de Ingenieria and CONICET, Universidad Nacional del Comahue, Neuquen 8300, Argentina"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,22]]},"reference":[{"key":"ref_1","unstructured":"Pearson, J.M. (1966). 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