Thermodynamics and Equations of State for Matter

The following sections are included:

• Preface
• Contents

The equation of state (EOS) which is a functional dependence between the parameters characterizing the state of matter is its basic quantitative characteristic permitting the application of the general formal apparatus of thermodynamics and continuous media dynamics (mathematical physics) to physical objects and processes of extremely diverse nature from thermal machines and biological structures to ultra-extreme conditions of Big Bang and relativistic hadron collisions…

As a substance advances along the scale of pressures and temperatures, its composition, structure, properties, etc. undergo radical changes from the ideal state of noninteracting neutral particles described by the classical statistical Boltzmann function to the exotic forms of baryon and quark– gluon matter some of whose features now began to show up in record-parameter experiments on relativistic ion collisions [294, 295] and manifest themselves in the interpretation of astronomical observations of so-called “compact” (“neutron” and “strange”) stars [414].

The pressures and temperatures realized in nature are presented schematically in Fig. 1.1.

In the second section of this chapter we shall touch upon ultrahigh compressions when the nuclear properties of matter come out to the foreground.

Gaseous and liquid states of matter are of greatest importance in everyday life of people and occupy a rather wide portion of the phase diagram (Figs. 2.1 and 2.2) [656]. From a solid body these states of matter are separated by a clearly pronounced interface with melting which, according to paper [598], has no critical point. In the range of high temperatures and pressures, the gas and liquid border upon the plasma emerging as a result of thermal ionization (T-ionization) or pressure-induced ionization (p-ionization). The boundary is here rather conditional and depends strongly on the quantum-chemical specificity of a particular substance (its ionization potential, electron structure, atomic size, etc.)…

The following sections are included:

• Hartree and Hartee–Fock approximations
• Asphericity of cells
• Pseudopotential models

The following sections are included:

• Historical remarks
• Hierarchy of models
• Chemical model. Dimensionless parameters
• Physical model. Thermodynamic relations
• Thermodynamics of nonideal solar plasma
• Bound atom model
• Thermodynamic calculations
• Thermodynamics of shock compressed plasma of megabar pressures. Nonideality and degeneracy
• Gas thermodynamics
• Hydrogen thermodynamics
• Metal plasma thermodynamics

The following sections are included:

• Monte Carlo method. Pseudopotentials
• Quantum MCM. Path integrals
• H and H + He plasmas
• Shock adiabat of deuterium
• Electron–hole plasma of semiconductors
• Crystallization of holes
• Electron–hole plasma of germanium
• Quantum MD
• QGP simulations

In the previous chapters, we saw that the description of thermodynamic, structural, and transport properties of real substances requires a correct quantum-mechanical calculation of the wave functions and the energy spectra of many-electron systems, which in the general case encounters great computational difficulties in solution of the quantum-mechanical many-body problem. This necessitates the introduction of simplifying assumptions underlying the modern condensed state models considered in the two chapters to follow. To begin, we shall review some history which will be presented in line with the perfect work [801].

The following sections are included:

• Density functional method
• Atomic and molecular structures
• Condensed media

The consideration of various models of the thermodynamic description of matter physical properties makes it clear that the conventional classification of states in the high-pressure and high-temperature region often loses its definiteness and becomes conditional. The phase boundaries either vanish or become smeared and actually correspond to continuous mutual transformation of the close states. In this chapter, we will consider the relationships between different phases of matter. This will help to present in a more definite way the general form of the phase diagram taking into account the real and hypothetical phase transitions.

It follows from the previous chapters that the description of the thermodynamic properties of nonideal media requires the application of complicated models which, due to their narrow specialization, can be used in a limited range of matter state parameters. As a rule, these models incorporate cumbersome quantum-mechanical numerical calculations and provide information in the form of diagrams or big tables that makes it difficult to use these data in practical calculations. Such equations of state (EOS) are sometimes called “global” [1002]. They are generally based on using modern powerful theoretical models for the calculation of the separate domains of the phase diagram. The obtained tables of the thermodynamic functions should be then smoothly sewed by means of the interpolation procedure…

In this chapter, following Ref. [414] we will consider the thermodynamic description of the electromagnetic (Coulomb) plasma arising in various astrophysical objects — in white, brown, and yellow dwarfs, red giants, and neutron and quark–gluon stars…

Figure 11.1 shows the characteristic dimensions and times of the motion of molecular, atomic, and nuclear objects [525], and Fig. 11.2 shows the characteristic dimensions of different structural substance states. Because atomic and nuclear dimensions differ by 5–6 orders of magnitude away from nuclear densities ρ ≪ ρ₀ ≈ 2.8 · 10¹⁴ g/cm³, these processes may be treated independently. Despite the fact that they are, of course, rigidly bound for any ρ, since the nuclear structure and charge directly define the electron structure of an atom or ion as well as its chemical properties and the aggregate substance state…

The Equation of State (EOS) of degenerate hadronic matter becomes substantially simpler in the limit of high densities. Quarks are no longer bound in hadrons and constitute a weakly interacting Fermi gas [189].

In this chapter, we will follow Ref. [667]. First of all, note that the very concept of “nuclear matter” as an infinite homogeneous system consisting of nucleons is sort of conventional. In practice, we deal with the nuclei which have up to N ≈ 300 nucleons and the concept of nuclear matter is an approximation of their interior domains. A prolonged nuclear matter presumably arises in neutron and quark stars and at the early stages of the Big Bang…

The following sections is included:

• Bibliography