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8.333

Statistical Mechanics I

4-0-8 units · Graduate

First part of a two-subject sequence on statistical mechanics. Examines the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, microcanonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory.

Fall 2013 · Statistical Mechanics I: Statistical Mechanics of Particles

Topics

  • Fundamental Definitions, The Zeroth Law, The First Law
  • The Second Law, Carnot Engines and Thermodynamic Temperature, Entropy
  • Approach to Equilibrium and Thermodynamic Potentials, Useful Mathematical Results
  • Stability Conditions, The Third Law
  • General Definitions, One Random Variable, Some Important Probability Distributions
  • Recitation
  • Many Random Variables, Sums of Random Variables and the Central Limit Theorem, Rules for Large Numbers, Information, Entropy, and Estimation
  • General Definitions, Liouville’s Theorem
  • The Bogoliubov-Born-Green-Kirkwood-Yvon Hierarchy, The Boltzmann Equation
  • The H-Theorem and Irreversibility, Equilibrium Properties
  • Conservation Laws
  • Zeroth Order Hydrodynamics, First Order Hydrodynamics
  • General Definitions, The Microcanonical Ensemble, Two-Level Systems
  • The Ideal Gas, Mixing Entropy and Gibbs’ Paradox, The Canonical Ensemble
  • Examples, The Gibbs Canonical Ensemble, The Grand Canonical Ensemble
  • The Cumulant Expansion
  • The Cluster Expansion
  • The Second Virial Coefficient and Van der Waals Equation, Breakdown of the Van der Waals Equation, Mean Field Theory of Condensation
  • Variational Methods, Corresponding States, Critical Point Behavior
  • Mean field theory of condensation, Corresponding states, Critical point behavior (from L17 & L18)
  • Dilute Polyatomic Gases, Vibrations of a Solid, Black-body Radiation
  • Quantum Microstates, Quantum Macrostates
  • Hilbert Space of Identical Particles
  • Canonical Formulation, Grand Canonical Formulation
  • The Degenerate Fermi Gas
  • The Degenerate Bose Gas
  • Superfluid He 4

Readings

Prerequisites & course information

Prereq: 8.044 and 8.05 G (Fall) 4-0-8 units

Sources