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arXiv · 2301.11016

On the Thermodynamics of Particles Obeying Monotone Statistics

Fabio Ciolli·Francesco Fidaleo·Chiara Marullo
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Abstract

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.

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Fabio Ciolli, Francesco Fidaleo, Chiara Marullo. 2023-01-26. On the Thermodynamics of Particles Obeying Monotone Statistics. https://doi.org/10.3390/e25020216

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