MIT 8.333: Mehran Kardar - Statistical Mechanics I
Graduate-level statistical mechanics with mathematical rigor - 16 comprehensive lectures
About This Series
Professor Mehran Kardar from MIT delivers a rigorous graduate-level course on statistical mechanics. These lectures form the basis of his widely-used textbook "Statistical Physics of Particles" and provide deep mathematical foundations alongside physical insight.
This is MIT's 8.333 Statistical Mechanics I course, covering thermodynamics, kinetic theory, classical statistical mechanics, and interacting particle systems. Kardar's approach emphasizes mathematical formalism, making it the perfect complement to Susskind's intuitive lectures.
Why Kardar + Susskind Together?
- • Complementary Approaches: Susskind (intuition) + Kardar (rigor) = complete understanding
- • Mathematical Depth: Kardar derives everything from first principles with full mathematical detail
- • Textbook Alignment: Based on Kardar's renowned textbook, widely used in graduate programs
- • Graduate Level: Preparation for research in condensed matter, QFT, plasma physics
- • Complete Coverage: 26 total lectures (10 Susskind + 16 Kardar) cover entire StatMech curriculum
Level
First-year graduate. Assumes undergraduate physics and strong mathematical background.
Duration
16 lectures from MIT OCW, approximately 1.5 hours each
Textbook
Statistical Physics of Particles by Mehran Kardar (Cambridge University Press)
Topics Covered
Thermodynamics (4 lectures)
- • Thermodynamic systems and laws
- • Equilibrium and state variables
- • Entropy and second law
- • Thermodynamic potentials
- • Maxwell relations and response functions
Probability (2 lectures)
- • Probability distributions and moments
- • Central limit theorem
- • Random walks and diffusion
- • Gaussian distributions
- • Generating functions
Kinetic Theory (5 lectures)
- • Boltzmann equation and H-theorem
- • Maxwell-Boltzmann distribution derivation
- • Transport coefficients
- • Mean free path and collision theory
- • Hydrodynamic limit
Classical Statistical Mechanics (3 lectures)
- • Phase space and Liouville's theorem
- • Microcanonical ensemble in depth
- • Canonical ensemble and partition function
- • Grand canonical ensemble formalism
- • Ideal gas from first principles
Interacting Particles (2 lectures)
- • Van der Waals equation of state
- • Cluster expansions
- • Virial coefficients
- • Phase transitions introduction
- • Mean field theory
Kardar vs Susskind: How to Use Both
These two lecture series are highly complementary. Here's how to use them together effectively:
Susskind (Intuition)
- ✓ Physical intuition and motivation
- ✓ "Why" behind the mathematics
- ✓ Accessible explanations
- ✓ Conceptual understanding
- ✓ Great for first pass
Kardar (Rigor)
- ✓ Mathematical formalism and proofs
- ✓ Detailed derivations
- ✓ Graduate-level depth
- ✓ Preparation for research
- ✓ Essential for problem-solving
→ You're here! (Kardar lectures)
Recommended Study Strategy
- 1. First Pass (Susskind): Watch Susskind Lecture 1 → build intuition for thermodynamics
- 2. Deep Dive (Kardar): Watch Kardar Lectures 1-4 → rigorous thermodynamics derivations
- 3. Work Problems: Solve exercises from Kardar textbook or Pathria
- 4. Repeat: Continue pattern (Susskind for intuition → Kardar for rigor → problems)
- 5. Advanced Topics: Kardar's interacting particles prepares for Susskind's phase transitions
Complete Lecture Series
All 16 lectures from MIT 8.333 Statistical Mechanics I. These form the first semester of graduate statistical mechanics.
Part I: Thermodynamics (Lectures 1-4)
Foundation of statistical mechanics - laws of thermodynamics, entropy, and thermodynamic potentials
Thermodynamics Part 1
Introduction to thermodynamic systems, state variables, thermal equilibrium, zeroth law, temperature definition
Video Lecture
Thermodynamics Part 1
Introduction to thermodynamics and equilibrium
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Thermodynamics Part 2
First law (energy conservation), work and heat, internal energy U, enthalpy H, heat capacities CV and CP
Video Lecture
Thermodynamics Part 2
First law of thermodynamics and thermodynamic processes
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Thermodynamics Part 3
Second law, Carnot cycle, entropy S, irreversibility, entropy increase principle, temperature-entropy diagrams
Video Lecture
Thermodynamics Part 3
Second law of thermodynamics and entropy
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Thermodynamics Part 4
Thermodynamic potentials (U, H, F, G), Maxwell relations, response functions, stability criteria
Video Lecture
Thermodynamics Part 4
Thermodynamic potentials and Maxwell relations
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Part II: Probability Theory (Lectures 5-6)
Mathematical foundations - probability distributions, random walks, and central limit theorem
Probability Part 1
Probability distributions, moments (mean, variance), generating functions, binomial and Poisson distributions
Video Lecture
Probability Part 1
Probability theory fundamentals and distributions
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Probability Part 2
Central limit theorem, Gaussian distributions, random walks, diffusion equation, Langevin dynamics
Video Lecture
Probability Part 2
Central limit theorem and random walks
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Part III: Kinetic Theory of Gases (Lectures 7-11)
Microscopic foundations - Boltzmann equation, Maxwell-Boltzmann distribution, transport theory
Kinetic Theory Part 1
Microscopic vs macroscopic description, phase space density, Boltzmann equation introduction
Video Lecture
Kinetic Theory of Gases Part 1
Introduction to kinetic theory and phase space
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Kinetic Theory Part 2
Boltzmann H-theorem, approach to equilibrium, irreversibility, entropy in kinetic theory
Video Lecture
Kinetic Theory of Gases Part 2
H-theorem and irreversibility
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Kinetic Theory Part 3
Derivation of Maxwell-Boltzmann distribution, equilibrium solution, velocity distribution functions
Video Lecture
Kinetic Theory of Gases Part 3
Maxwell-Boltzmann distribution derivation
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Kinetic Theory Part 4
Transport coefficients (viscosity, thermal conductivity, diffusion), mean free path, collision theory
Video Lecture
Kinetic Theory of Gases Part 4
Transport coefficients and collision theory
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Kinetic Theory Part 5
Hydrodynamic limit, Navier-Stokes equations from Boltzmann equation, conservation laws
Video Lecture
Kinetic Theory of Gases Part 5
Hydrodynamic limit and Navier-Stokes equations
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Part IV: Classical Statistical Mechanics (Lectures 12-14)
Ensemble theory - microcanonical, canonical, and grand canonical ensembles with rigorous derivations
Classical Statistical Mechanics Part 1
Liouville's theorem, ergodicity, microcanonical ensemble, entropy S = kB ln Ω derivation
Video Lecture
Classical Statistical Mechanics Part 1
Liouville's theorem and microcanonical ensemble
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Classical Statistical Mechanics Part 2
Canonical ensemble, partition function Z(β), connection to thermodynamics, free energy F = -kBT ln Z
Video Lecture
Classical Statistical Mechanics Part 2
Canonical ensemble and partition function
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Classical Statistical Mechanics Part 3
Grand canonical ensemble, chemical potential μ, grand partition function Ξ, ideal gas applications
Video Lecture
Classical Statistical Mechanics Part 3
Grand canonical ensemble and applications
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Part V: Interacting Particles (Lectures 15-16)
Beyond ideal gases - interactions, virial expansion, phase transitions introduction
Interacting Particles Part 1
Van der Waals equation, cluster expansion, virial coefficients, corrections to ideal gas law
Video Lecture
Interacting Particles Part 1
Van der Waals equation and cluster expansion
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Interacting Particles Part 2
Phase transitions, coexistence curves, critical points, mean field theory introduction, Landau theory
Video Lecture
Interacting Particles Part 2
Phase transitions and mean field theory
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Study Guide & Tips
📝 Before Each Lecture
- • Read corresponding chapter in Kardar's textbook (if available)
- • Review prerequisite mathematics (probability, calculus, differential equations)
- • Have pen and paper ready - these are derivation-heavy lectures
- • Set up 2-3 hour blocks - lectures are dense and reward deep focus
✏️ During Each Lecture
- • Pause frequently and rederive equations yourself
- • Note assumptions and approximations being made
- • Pay attention to mathematical techniques (Lagrange multipliers, steepest descent, etc.)
- • Track physical units to catch errors
- • Write down key results in your own notation
🔬 After Each Lecture
- • Work through problem sets from Kardar's textbook
- • Rederive key results from memory
- • Compare with Susskind's approach for same topic
- • Look up alternative derivations in Pathria or Huang
- • Apply to simple systems (harmonic oscillator, two-level system, etc.)
🎯 Key Concepts to Master
- Thermodynamics: All four laws, Maxwell relations, thermodynamic potentials
- Probability: Central limit theorem, Gaussian integrals, generating functions
- Kinetic Theory: Boltzmann equation, H-theorem, transport coefficients
- Ensembles: Microcanonical, canonical, grand canonical - when to use each
- Calculations: Partition functions, free energies, thermodynamic derivatives
Textbook Alignment
These lectures follow Kardar's textbook "Statistical Physics of Particles" closely:
Lectures 1-4 → Kardar Chapters 1-2
Thermodynamics
Lectures 5-6 → Kardar Chapter 3
Probability Theory
Lectures 7-11 → Kardar Chapter 4
Kinetic Theory of Gases
Lectures 12-14 → Kardar Chapters 5-6
Classical Statistical Mechanics
Lectures 15-16 → Kardar Chapter 7
Interacting Particles
Other Recommended Textbooks
- • Pathria & Beale: More detailed, excellent problems, good supplement
- • Huang: Very rigorous, advanced topics, graduate level
- • Kittel & Kroemer: More accessible, good for parallel reading
- • Reif: Classic text, different organization, helpful alternative perspective
After Completing This Series
After mastering this material, you'll be well-prepared for:
Statistical Mechanics II (Kardar)
Quantum statistics, phase transitions, renormalization group, critical phenomena
→ Plasma Physics
Apply kinetic theory and Boltzmann equation to plasmas
→ Quantum Field Theory
Thermal field theory and finite temperature QFT
Condensed Matter Physics
Many-body systems, phase transitions, critical phenomena