理想夸子气体的热力学几何

中文摘要 AI 辅助

我们在巨正则系综中研究了理想夸子气体的平衡热力学和热力学黎曼几何。通过引入代数形变参数 $q$，该系统推广了标准玻色子行为，并在无形变极限下恢复为常规理想玻色气体。对基态占据的严格考察揭示了逸度的两个不连通的数学域。通过强制热力学连续性、单值性以及与高温经典极限的一致性，我们排除了第二个数学分支，并将较低区间确立为唯一物理上允许的状态空间。这将形变参数识别为内禀的广义玻色-爱因斯坦凝聚阈值。利用平衡参数流形上的Fisher-Rao度量，我们探测了所有温度范围内的热力学标量曲率。在整个物理域内，标量曲率保持严格为正，证实形变保留了有效吸引的统计相互作用，而未诱导费米子倾向。在临界凝聚阈值附近，曲率急剧增加并表现出明确的发散，为宏观相干性和临界涨落提供了明确的几何特征。在转变温度以下，逸度的钉扎消除了一个涨落自由度，使标量曲率坍缩为零。

英文摘要

We investigate the equilibrium thermodynamics and thermodynamic Riemannian geometry of an ideal quon gas within the grand canonical ensemble. By incorporating the algebraic deformation parameter $q$, the system generalizes standard bosonic behavior while recovering the conventional ideal Bose gas in the undeformed limit. A rigorous examination of the ground-state occupation reveals two disconnected mathematical domains of the fugacity. By enforcing thermodynamic continuity, single-valuedness, and consistency with the high-temperature classical limit, we exclude the second mathematical branch and establish the lower interval as the unique physically admissible state space. This identifies the deformation parameter as an intrinsic, generalized Bose--Einstein condensation threshold. Employing the Fisher-Rao metric on the equilibrium parameter manifold, we probe the thermodynamic scalar curvature across all temperature regimes. The scalar curvature remains strictly positive throughout the physical domain, confirming that the deformation preserves an effectively attractive statistical interaction without inducing fermionic tendencies. Near the critical condensation threshold, the curvature increases sharply and exhibits a definitive divergence, providing an unambiguous geometric signature of macroscopic coherence and critical fluctuations. Below the transition temperature, the pinning of fugacity eliminates a fluctuating degree of freedom, collapsing the scalar curvature to zero.

发表机构

• University of Mohaghegh Ardabili（莫哈格赫阿尔达比勒大学）

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