发表机构
University of Mohaghegh Ardabili（莫哈格赫阿尔达比勒大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究负统计参数包含统计理想量子气体的热力学几何，发现曲率恒正且发散处对应凝聚相变，凝聚温度高于玻色气体，并在低维区间出现有限温度凝聚。
AI 中文摘要
我们研究了服从包含统计的理想量子气体的热力学几何，该统计以负统计参数 $g < 0$ 为特征。在此框架下，巨正则配分函数允许有限的最大逸度，且对于所有 $g < 0$，热力学标量曲率 $R$ 严格为正，反映了与玻色子系统类似的有效吸引统计相互作用。当逸度接近其最大值时，$R$ 发散，标志着玻色-爱因斯坦凝聚型相变的发生。与普通理想玻色气体的一个关键区别在于，凝聚温度相对于玻色子情形有所升高，并且在标准玻色子不凝聚的维度区间 $1/2 < D/\sigma \leq 1$ 内，有限温度凝聚也会发生，而对于 $D/\sigma \leq 1/2$，转变温度消失。三个独立判据：$R$ 的发散、最大逸度奇异性以及比热中的非解析尖点，在相同凝聚点处重合，证实了该转变的热力学一致性。
英文摘要
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 $1/2 < D/σ\leq 1$ where standard bosons do not condense, while for $D/σ\leq 1/2$ 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.
