On the Thermodynamics of Particles Obeying Monotone Statistics
| Autor: | Ciolli, Fabio, Fidaleo, Francesco, Marullo, Chiara |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Entropy 2023, 25(2), 216 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3390/e25020216 |
| Popis: | 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 "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. Comment: Published in Entropy, 2 Figures |
| Databáze: | arXiv |
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