{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:48:18Z","timestamp":1760147298969,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,22]],"date-time":"2023-01-22T00:00:00Z","timestamp":1674345600000},"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>The aim of the present paper is to provide a preliminary investigation of the thermodynamics of particles obeying monotone statistics. To render the potential physical applications realistic, we propose a modified scheme called block-monotone, based on a partial order arising from the natural one on the spectrum of a positive Hamiltonian with compact resolvent. The block-monotone scheme is never comparable with the weak monotone one and is reduced to the usual monotone scheme whenever all the eigenvalues of the involved Hamiltonian are non-degenerate. Through a detailed analysis of a model based on the quantum harmonic oscillator, we can see that: (a) the computation of the grand-partition function does not require the Gibbs correction factor n! (connected with the indistinguishability of particles) in the various terms of its expansion with respect to the activity; and (b) the decimation of terms contributing to the grand-partition function leads to a kind of \u201cexclusion principle\u201d analogous to the Pauli exclusion principle enjoined by Fermi particles, which is more relevant in the high-density regime and becomes negligible in the low-density regime, as expected.<\/jats:p>","DOI":"10.3390\/e25020216","type":"journal-article","created":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T02:27:45Z","timestamp":1674440865000},"page":"216","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Thermodynamics of Particles Obeying Monotone Statistics"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4364-3829","authenticated-orcid":false,"given":"Fabio","family":"Ciolli","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica e Informatica, Universit\u00e0 della Calabria, Via Pietro Bucci, Cubo 30B, I-87036 Rende, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6807-2826","authenticated-orcid":false,"given":"Francesco","family":"Fidaleo","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Roma Tor Vergata, Via della Ricerca Scientifica, 1, I-00133 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0913-4481","authenticated-orcid":false,"given":"Chiara","family":"Marullo","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica \u201cGuido Castelnuovo\u201d, Sapienza Universit\u00e0 di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1007\/s002200050126","article-title":"The spectral action principle","volume":"186","author":"Chamseddine","year":"1997","journal-title":"Commun. 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