CLASSICAL STATISTICAL MECHANICS

 Prof. Lev Pitaevskii

PROGRAMME

1. KINETIC THEORY OF GAZES
Phase space and distribution function. KH 3.1; LP 1, 2.
Continuity equation in the phase space. KH 4.3; LL5 3.
Boltzmann kinetic equation in the absence of collisions. General solution of the equation.
Collisionless motion of a gas. Expansion of the gas in vacuum. Decay of initial perturbation of density. LP 15 (Problem 1).
Integral of collisions. General properties of the integral. (Laws of conservation.)KH 5.2; LP 5.
Derivation of the equations of motion of an ideal gas from the Boltzmann equation. Entropy conservation. KH 5.3; LP 5.
Explicit expression for the collisional integral. Probability of scattering.  Time reversal and space inversion. Effective integral of collisions. KH 3.2, 3.3; LP 3.
Boltzmann H-theorem. KH 4.1; LP 4.
Effective cross-section of scattering. KH 3.2.
Viscosity and thermoconductivity. Navier-Stokes equations. KH 5.6, 5.7; LL6 15.
Equations for a correction to the equilibrium distribution function for slightly inhomogeneous gas in presence of  gradient of temperature or gradients of velocity. KH 5.4, 6.1; LP 6,7,8.
Calculation of the coefficients of viscosity and thermoconductivity for effective collisional integral. KH 5.4, 5.5.
Diffusion. Coefficients of diffusion and mobility. Einstein equation.  Electroconductivity.  LP 11, 12; LL6 80.
Integral of collisions of light atoms with heavy atoms. Calculation of the coefficient of mobility. Electroconductivity of plasma. Debye length and Coulomb logarithm. LP 11.
Coefficient of diffusion for small particles in a light gas. LL6 80.
Number of microscopical states for a given macroscopical state. Physical meaning of the entropy. KH 4.4; LL5 40.
Explanation of the irreversibility from microscopical point of view. Fluctuations. KH 4.4, 4.5
Plasma waves and Landau damping. LP 29, 32. (Optional)
2. PHENOMENOLOGICAL THERMODYNAMICS
Work, quantity of heat and entropy. KH 1.1, 1.2, 1.3; LL5 13.
Free energy and thermodynamic potential KH 1.6; LL5 15.
Relations between the derivatives of thermodynamic quantities LL5 16.
Thermodynamic scale of temperature LL5 17.
Chemical potential KH 2.1, 7.5; LL5 24.
Phase transitions of the first order. KH 2.1, 2.2;LL5 81, 82.
3. GIBBS METHOD
Time averaging and distribution function. LL5 2.
Liouville's theorem KH 3.4; LL5 3.
Microcanonical and canonical (Gibbs) distributions. KH 6.2, 7.1; LL5 4, 28.
Free energy in the Gibbs distribution. LL5 31.
Equation of state of an ideal gas. LL5 42.

REFERENCE TEXTS
KH - K. Huang, Statistical Mechanics (Meccanica Statistica
LL5 - L.D. Landau, E.M. Lifshitz,  Statistical Physics, Part. 1
LL6 - L.D. Landau, E.M. Lifshitz, Fluid Mechanics
LP - E.M. Lifshitz, L.P. Pitaevskii, Physical Kinetics

Numbers mean numbers of relevant sections of the books.