Thermodynamic geometry of inclusion statistics
Abstract
We investigate the thermodynamic geometry of an ideal quantum gas obeying inclusion statistics, characterized by a negative statistical parameter g < 0. In this framework the grand-canonical partition function admits a finite maximum fugacity, and the thermodynamic scalar curvature R is strictly positive for all g < 0, reflecting effective attractive statistical interactions analogous to those of a bosonic system. As the fugacity approaches its maximum value, R diverges, signaling a phase transition of the Bose-Einstein condensation type. A key distinction from the ordinary ideal Bose gas is that the condensation temperature is elevated relative to the bosonic case, and finite-temperature condensation occurs even in the dimensional regime 1/2 < D/σ≤ 1 where standard bosons do not condense, while for D/σ≤ 1/2 the transition temperature vanishes. Three independent criteria; divergence of R, the maximum fugacity singularity, and the non-analytic cusp in the specific heat, coincide at the same condensation point, confirming the thermodynamic consistency of the transition.
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BibTeX
@misc{ardabili2026thermodynamic,
title = {{Thermodynamic geometry of inclusion statistics}},
author = {M. H. Naghizadeh Ardabili and Omid Yahyayi Monem and Habib Esmaili and Zahra Ebadi and Hosein Mohammadzadeh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13787},
eprint = {2609.13787},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13787},
}
RIS
TY - UNPB
TI - Thermodynamic geometry of inclusion statistics
AU - M. H. Naghizadeh Ardabili
AU - Omid Yahyayi Monem
AU - Habib Esmaili
AU - Zahra Ebadi
AU - Hosein Mohammadzadeh
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13787
UR - https://arxiv.org/abs/2609.13787
AB - We investigate the thermodynamic geometry of an ideal quantum gas obeying inclusion statistics, characterized by a negative statistical parameter g < 0. In this framework the grand-canonical partition function admits a finite maximum fugacity, and the thermodynamic scalar curvature R is strictly positive for all g < 0, reflecting effective attractive statistical interactions analogous to those of a bosonic system. As the fugacity approaches its maximum value, R diverges, signaling a phase transition of the Bose-Einstein condensation type. A key distinction from the ordinary ideal Bose gas is that the condensation temperature is elevated relative to the bosonic case, and finite-temperature condensation occurs even in the dimensional regime 1/2 < D/σ≤ 1 where standard bosons do not condense, while for D/σ≤ 1/2 the transition temperature vanishes. Three independent criteria; divergence of R, the maximum fugacity singularity, and the non-analytic cusp in the specific heat, coincide at the same condensation point, confirming the thermodynamic consistency of the transition.
ER -