The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei
The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei
复制标题
物质的构成：由电子和原子核组成的系统热力学的存在性
DOI：
10.1007/978-3-662-10018-9_3
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发表时间：
1972
影响因子：
1.7
通讯作者：
J. Lebowitz
中科院分区：
文献类型：
--
作者：
E. Lieb;J. Lebowitz
我们建立了带电粒子系统的自由能密度的无限体积（热力学）极限的存在性，例如，电子和原子核。这些粒子是宏观物质的基本成分，它们通过库仑力相互作用。这种相互作用的长程性质需要使用新的方法来证明极限的存在。结果表明，极限函数具有宏观热力学所要求的所有凸性（稳定性）性质。对于电中性系统，极限函数是域形状无关的，而对于具有净电荷的系统，热力学自由能密度是形状相关的，符合经典静电学的众所周知的公式。分析是基于统计力学系综形式主义的吉布斯，可以是经典的或量子力学。证明了微正则系综、正则系综和巨正则系综的等价性。
We establish the existence of the infinite volume (thermodynamic) limit for the free energy density of a system of charged particles, e.g., electrons and nuclei. These particles, which are the elementary constituents of macroscopic matter, interact via Coulomb forces. The long range nature of this interaction necessitates the use of new methods for proving the existence of the limit. It is shown that the limit function has all the convexity (stability) properties required by macroscopic thermodynamics. For electrically neutral systems, the limit functions is domain-shape independent, while for systems having a net charge the thermodynamic free energy density is shape dependent in conformity with the well-known formula of classical electrostatics. The analysis is based on the statistical mechanics ensemble formalism of Gibbs and may be either classical or quantum mechanical. The equivalence of the microcanonical, canonical and grand canonical ensembles is demonstrated.