Lim Yu Rim, Park Seong Jun, Song Sanggeun, Yang Gil-Suk, Yoon Young-Gui, Kim Ji-Hyun, Sung Jaeyoung
Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea.
Department of Physics, Chung-Ang University, Seoul 156-756, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062131. doi: 10.1103/PhysRevE.89.062131. Epub 2014 Jun 25.
Liquid helium does not obey the Gibbs fluctuation-compressibility relation, which was noted more than six decades ago. However, still missing is a clear explanation of the reason for the deviation or the correct fluctuation-compressibility relation for the quantum liquid. Here we present the fluctuation-compressibility relation valid for any grand canonical system. Our result shows that the deviation from the Gibbs formula arises from a nonextensive part of thermodynamic potentials. The particle-exchange symmetry of many-body wave function of a strongly degenerate quantum gas is related to the thermodynamic extensivity of the system; a Bose gas does not always obey the Gibbs formula, while a Fermi gas does. Our fluctuation-compressibility relation works for classical systems as well as quantum systems. This work demonstrates that the application range of the Gibbs-Boltzmann statistical thermodynamics can be extended to encompass nonextensive open systems without introducing any postulate other than the principle of equal a priori probability.
液氦并不遵循吉布斯涨落 - 压缩性关系，这在六十多年前就已被注意到。然而，对于这种偏差的原因或量子液体正确的涨落 - 压缩性关系，仍然缺乏清晰的解释。在此，我们给出适用于任何巨正则系统的涨落 - 压缩性关系。我们的结果表明，与吉布斯公式的偏差源于热力学势的非广延部分。强简并量子气体多体波函数的粒子交换对称性与系统的热力学广延性相关；玻色气体并不总是遵循吉布斯公式，而费米气体则遵循。我们的涨落 - 压缩性关系适用于经典系统以及量子系统。这项工作表明，吉布斯 - 玻尔兹曼统计热力学的应用范围可以扩展到涵盖非广延开放系统，而无需引入除先验概率相等原则之外的任何假设。
