关于量子环境不变性和交换对称性的统计力学评论
Comment on Statistical mechanics from quantum envariance and exchange symmetry
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中文总结 AI 辅助
本文评论了Ojha等人关于统计力学的观点，指出其结论不成立，如约化密度矩阵有误、熵条件不满足等，通过双粒子计算显化矛盾，还指出萨哈部分问题，给出修正公式并确定不受影响的结果。
中文摘要 AI 辅助
Ojha、Sardana和Ghosh [《物理评论A》113, 042221 (2026)] 提出，追踪粒子排列的环境记录会产生熵\(k_B\ln N!\)，从而解释吉布斯因子，并使用相同结构将萨哈平衡关系乘以\(1/(N_e!N_p!)\)。我们表明这些结论并不成立。他们式(32)中的约化密度矩阵不是偏迹，即使在自然修正解释下，只有当系统分支态相互正交时熵才等于\(k_B\ln N!\)。该条件一般不满足，且施加于标记排列分支时，本身并不将粒子态限制在一个玻色或费米对称扇区。双粒子计算使矛盾显化。他们的吉布斯佯谬计算也从可区分粒子熵出发却称之为萨库尔 - 泰特罗德熵。在萨哈部分，式(52)所写状态可分解且系统 - 环境纠缠为零。所提出的阶乘在声称的稀薄气体极限下不趋近于1，不产生有限非零强度热力学极限，且对不可区分性计数两次。我们给出修正的正则和基于逸度的公式，并确定论文中哪些标准结果不受影响。
英文摘要
Ojha, Sardana, and Ghosh [Phys. Rev. A 113, 042221 (2026)] propose that tracing environmental records of particle permutations produces an entropy kB ln N!, thereby explaining the Gibbs factor, and use the same construction to multiply the Saha equilibrium relation by 1/(Ne!Np!). We show that these conclusions do not follow. The reduced density matrix printed in their Eq. (32) is not a partial trace, and even under the natural corrected interpretation the entropy equals kB ln N! only when the system branch states are mutually orthogonal. That condition is not generally satisfied and, when imposed on labeled permutation branches, does not by itself restrict the particle state to one bosonic or fermionic symmetry sector. A two-particle calculation makes the contradiction explicit. Their Gibbs-paradox calculation also starts from a distinguishable-particle entropy while calling it the Sackur-Tetrode entropy. In the Saha section, the state in Eq. (52), as written, factorizes and has zero system-environment entanglement. The proposed factorial does not approach unity in the claimed dilute-gas limit, does not yield a finite nonzero intensive thermodynamic limit, and counts indistinguishability twice. We give the corrected canonical and fugacity-based formulations and identify which standard results of the paper remain unaffected.
