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Statistical Mechanics

These notes synthesize Franz Schwabl's graduate-level treatment of statistical mechanics into a wiki path from microscopic probability to equilibrium ensembles, quantum gases, interacting matter, critical phenomena, and nonequilibrium processes. The organizing idea is that thermodynamics is not replaced by mechanics; it is derived as the large-scale, high-dimensional consequence of microscopic laws plus statistical hypotheses about accessible states.

The section begins with probability, density matrices, phase-space flow, and the microcanonical postulate. It then builds the canonical and grand canonical ensembles, where partition functions generate thermodynamic potentials and fluctuations. The middle pages apply those tools to ideal gases, quantum statistics, degenerate Fermi systems, Bose condensation, radiation, phonons, real gases, molecular mixtures, magnetism, and phase coexistence. The later pages cover phase transitions, Landau theory, scaling, renormalization-group ideas, stochastic dynamics, response theory, kinetic transport, and irreversibility. Cross-links point to thermodynamics, quantum mechanics, probability, and quantum field theory where the same structures reappear.

  1. Probability and Density Matrices
  2. Phase Space, Liouville Theorem, and Ergodicity
  3. Microcanonical Ensemble and Entropy
  4. Canonical Ensemble and Fluctuations
  5. Grand Canonical Ensemble and Particle Exchange
  6. Classical Ideal Gas and Maxwell Distribution
  7. Quantum Statistics and Ideal Quantum Gases
  8. Degenerate Fermi Gas
  9. Bose Gases, Photons, and Phonons
  10. Thermodynamic Potentials and Phase Equilibrium
  11. Real Gases, Virial Expansion, and van der Waals Theory
  12. Molecular Gases, Mixtures, and Solutions
  13. Magnetism, Lattice Gases, and Binary Alloys
  14. Phase Transitions and Order Parameters
  15. Mean-Field and Landau Theory
  16. Scaling, Universality, and Renormalization Group
  17. Brownian Motion, Langevin, and Fokker-Planck Dynamics
  18. Linear Response, Fluctuation-Dissipation, and Onsager Theory
  19. Boltzmann Equation and Transport
  20. Irreversibility, Master Equations, and Finite-Temperature Field Theory