On the Thermodynamics of Particles Obeying Monotone Statistics
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 <i>block-monotone</i>, based on a partial order arising from...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/2/216 |
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| author | Fabio Ciolli Francesco Fidaleo Chiara Marullo |
| author_facet | Fabio Ciolli Francesco Fidaleo Chiara Marullo |
| author_sort | Fabio Ciolli |
| collection | DOAJ |
| description | 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 <i>block-monotone</i>, 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>!</mo></mrow></semantics></math></inline-formula> (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 “exclusion principle” 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. |
| first_indexed | 2024-03-11T08:51:28Z |
| format | Article |
| id | doaj.art-0cb41f66b18f47d49afc18ed76bd8799 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T08:51:28Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0cb41f66b18f47d49afc18ed76bd87992023-11-16T20:22:24ZengMDPI AGEntropy1099-43002023-01-0125221610.3390/e25020216On the Thermodynamics of Particles Obeying Monotone StatisticsFabio Ciolli0Francesco Fidaleo1Chiara Marullo2Dipartimento di Matematica e Informatica, Università della Calabria, Via Pietro Bucci, Cubo 30B, I-87036 Rende, ItalyDipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, I-00133 Roma, ItalyDipartimento di Matematica “Guido Castelnuovo”, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, ItalyThe 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 <i>block-monotone</i>, 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>!</mo></mrow></semantics></math></inline-formula> (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 “exclusion principle” 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.https://www.mdpi.com/1099-4300/25/2/216monotone grand-canonical ensemblethermodynamics of grand-canonical ensembleexclusion principlehigh- and low-density regimes |
| spellingShingle | Fabio Ciolli Francesco Fidaleo Chiara Marullo On the Thermodynamics of Particles Obeying Monotone Statistics Entropy monotone grand-canonical ensemble thermodynamics of grand-canonical ensemble exclusion principle high- and low-density regimes |
| title | On the Thermodynamics of Particles Obeying Monotone Statistics |
| title_full | On the Thermodynamics of Particles Obeying Monotone Statistics |
| title_fullStr | On the Thermodynamics of Particles Obeying Monotone Statistics |
| title_full_unstemmed | On the Thermodynamics of Particles Obeying Monotone Statistics |
| title_short | On the Thermodynamics of Particles Obeying Monotone Statistics |
| title_sort | on the thermodynamics of particles obeying monotone statistics |
| topic | monotone grand-canonical ensemble thermodynamics of grand-canonical ensemble exclusion principle high- and low-density regimes |
| url | https://www.mdpi.com/1099-4300/25/2/216 |
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