Statistical physics of interacting gases (Gibbs' formulation of equilibrium state
thermodynamics of interacting gases. Partition function. Mayer’s cluster expansion. Virial
expansion. Beth-Uhlenbeck approach to quantum gases. Equation of state of multicomponent
plasma with applications to stars. Chemical equilibrium and Saha equation. Gravitational
equilibrium of stars for different equations of state.) Statistical physics of quantized fields.
(The method of quantized fields. Low-temperature behavior of Bose gas, Bose-Einstein
condensation. Low-lying excitations in Fermi systems. Fermi-liquid theory. Equation of state
of degenerate matter, white dwarfs, and neutron stars. Weak equilibrium and change
neutrality conditions. Gravitational equilibrium of white dwarfs and neutron stars.) Phase
transitions (Phase transitions in Van-der-Waals gas. Lattice models. Spontaneous
magnetization of a ferromagnet. Lattice gas and binary alloys. Ising model in the Bethe
approximation. Critical exponents. Thermodynamic inequalities. Landau’s theory of second-
order phase transitions. Crystallization of white dwarf matter. Phase transitions from hadronic
to quark matter in neutron stars.) Renormalization group approach (Basic scalings. Simple
examples of renormalization. General formation of renormalization group equations.
Fluctuation-dissipation theorem. Linear response theory. Photon and neutrino interactions in
the stellar matter within the linear response theory.) Fluctuations (Thermodynamic
fluctuations. Spatial correlations. Fluctuation analysis on the example of Brownian motion.
Statistical physics of nuclear reaction in stars, pycnonuclear reactions in neutron stars.)
