title: Exchange symmetry, fluctuation-compressibility relation, and thermodynamic potentials of quantum liquids.
abstract: 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.
authors.affiliation: Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea.
authors.forename: Yu Rim
authors.initials: YR
authors.lastname: Lim
authors.affiliation: Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea.
authors.forename: Seong Jun
authors.initials: SJ
authors.lastname: Park
authors.affiliation: Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea.
authors.forename: Sanggeun
authors.initials: S
authors.lastname: Song
authors.affiliation: Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea.
authors.forename: Gil-Suk
authors.initials: GS
authors.lastname: Yang
authors.affiliation: Department of Physics, Chung-Ang University, Seoul 156-756, Korea.
authors.forename: Young-Gui
authors.initials: YG
authors.lastname: Yoon
authors.affiliation: Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea.
authors.forename: Ji-Hyun
authors.initials: JH
authors.lastname: Kim
authors.affiliation: Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea.
authors.forename: Jaeyoung
authors.initials: J
authors.lastname: Sung
mesh_terms: D019277:Entropy; D005740:Gases; D015233:Models, Statistical; D011789:Quantum Theory; D013816:Thermodynamics
chemical_list: D005740:Gases