{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T04:23:57Z","timestamp":1781065437635,"version":"3.54.1"},"reference-count":39,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T00:00:00Z","timestamp":1776124800000},"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>Area-law entropy appears in local quantum ground states, low-temperature Gibbs states, and gravitational physics, whereas classical thermodynamics is formulated with volume-extensive entropy. We propose a coarse-grained information-theoretic framework, based on an effective free-energy functional combining Fisher information, a potential term, and Shannon entropy, that organises these different scalings within a single thermodynamic picture. Comparing localisation costs, external stabilisation, and gravitational self-interaction at the level of scaling reveals three regimes. At microscopic scales, locality and low-temperature coherence enforce area-type entropy scaling. At intermediate scales, volume-law entropy emerges as an effective regime sustained by non-gravitational confinement or external support; in the absence of such support, volume-extensive entropy does not by itself define an intrinsically stable equilibrium. At large scales dominated by gravitational self-interaction, a reduced scaling analysis identifies area-type behaviour as the distinguished infrared scaling, consistent with black-hole thermodynamics and with macroscopic universality requirements. The framework clarifies the limited domain of classical extensivity and offers a unified coarse-grained perspective on the recurrence of area-law scaling across quantum and gravitational settings.<\/jats:p>","DOI":"10.3390\/e28040444","type":"journal-article","created":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T14:24:58Z","timestamp":1776176698000},"page":"444","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Volume-Law Entropy as a Mesoscopic Anomaly"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-0362-7300","authenticated-orcid":false,"given":"Lamine","family":"Bougueroua","sequence":"first","affiliation":[{"name":"Independent Researcher, London KT6 6DY, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"P08024","DOI":"10.1088\/1742-5468\/2007\/08\/P08024","article-title":"An area law for one-dimensional quantum systems","volume":"2007","author":"Hastings","year":"2007","journal-title":"J. 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