Necessary conditions of the equivalence of canonical and grand canonical ensembles in Coulomb system thermodynamics

Abstract

It was found that the equivalence of the grand canonical and canonical ensembles for the Coulomb systems is possible only when charged particles of different types in calculating the physical quantities are considered as formally “independent” ones, and the quasi-neutrality condition is used in the final stage of calculations. The phase equilibrium condition is obtained and the expression is derived for the isothermal compressibility of matter as a two-component Coulomb system, which corresponds to the known limit relations for static structure factors. On this basis, it is demonstrated that the critical point of matter, considering as the Coulomb system is determined from the condition of vanishing mean square of fluctuations of the total charge per unit volume.

Critical opalescence and the true dielectric state in a Coulomb system

“…Большой термодинамический потенциал Ω(T, V, {µ c }), отвечающий рассмотре-нию КС с использованием большого канонического распределения Гиббса, удовле-творяет соотношениям [36] …”

“…Эта задача ре-шена в работе [32] на основе точных предельных соотношений для корреляционных функций в длинноволновом пределе для квантовой двухкомпонентной КС, соот-ветствующей веществу, состоящему из одного химического элемента (ядер одного сорта) [33]- [35]. Соответствующее рассмотрение проводится с применением методов квантовой теории поля (диаграммной техники теории возмущений) с учетом особен-ностей использования большого канонического распределения Гиббса для КС [36].…”

Critical opalescence and the true dielectric state in a Coulomb system

“…This problem was solved in [32] based on point limit relations for the correlation functions in the long-range limit for a quantum two-component CS, which corresponds to a substance consisting of one chemical element (single-type nuclei) [33]- [35]. The corresponding consideration is based on the methods of quantum field theory (the diagram technique in perturbation theory) with specific features of using the grand canonical Gibbs distribution for CS taken into account [36].…”

Metal-nonmetal transition and the second critical point in expanded metals

“…Nevertheless, there exist a number of exact results [10][11][12][13] for solving the problem of the second critical point and its interrelation with the static conductivity. Using these results, we will show that two critical points can exist in the two-component CS consisting of electrons (subscript e) and nuclei of the one type (subscript c).…”

“…Only in this final expression, the quasi-neutrality condition (1) is used (see [13,14] for more details). We note that from the stability requirement the Coulomb system can be considered only within quantum statistics [9].…”