Kardar Statistical Mechanics Solutions
Solutions and video lectures for "Statistical Physics of Particles" and "Statistical Physics of Fields" by Mehran Kardar
About These Resources
Mehran Kardar's two-volume series is the modern standard for graduate statistical mechanics. MIT OpenCourseWare provides complete video lectures and problem solutions directly from the author.
MIT OCW Videos
26 lectures by Kardar himself
Official Solutions
From the textbook author
Problem Sets
MIT course assignments
MIT OpenCourseWare Video Lectures
Complete video lecture series from MIT's 8.333 Statistical Mechanics I taught by Prof. Mehran Kardar.
8.333 Statistical Mechanics of Particles
26 video lectures covering thermodynamics, probability, kinetic theory, classical and quantum statistical mechanics.
Topics Covered:
- • Thermodynamics fundamentals
- • Probability and statistics
- • Kinetic theory of gases
- • Classical statistical mechanics
- • Interacting particles
- • Quantum statistical mechanics
- • Ideal quantum gases
Course Materials:
- • 26 video lectures
- • Lecture notes (PDF)
- • Problem sets with solutions
- • Exam review materials
8.334 Statistical Mechanics of Fields
Advanced course covering collective behavior, phase transitions, renormalization group, and field theory methods.
Topics Covered:
- • Collective behavior
- • Mean-field theory
- • Landau-Ginzburg theory
- • Critical phenomena
- • Renormalization group
- • Path integrals
Prerequisites:
- • 8.333 (Stat Mech I)
- • Quantum Mechanics
- • Mathematical methods
Problem Solutions
Official and community solutions to problems from Kardar's textbooks.
Official Kardar Solutions
Problems and solutions compiled by Mehran Kardar for "Statistical Physics of Particles" - updated July 2008.
- • Chapter 1: Thermodynamics
- • Chapter 2: Probability
- • Chapter 3: Kinetic Theory
- • Chapter 4: Classical Stat Mech
- • Chapter 5: Interacting Particles
- • Chapter 6: Quantum Stat Mech
- • Chapter 7: Ideal Quantum Gases
MIT Exam & Problem Set Solutions
Complete problem sets and exam solutions from MIT's 8.333 course on OpenCourseWare.
- • Problem Set solutions
- • Midterm exam solutions
- • Final exam solutions
- • Exam review materials
Studocu Solutions
Community-contributed solutions to Statistical Mechanics of Particles problems.
View SolutionsDuke University Resources
Curated collection of statistical mechanics resources including Kardar materials.
Duke Stat Mech LinksKey Problem Topics
Thermodynamics
- • Equations of state
- • Maxwell relations
- • Thermodynamic potentials
- • Stability conditions
Statistical Ensembles
- • Microcanonical ensemble
- • Canonical ensemble
- • Grand canonical ensemble
- • Partition functions
Quantum Statistics
- • Fermi-Dirac distribution
- • Bose-Einstein distribution
- • Degenerate gases
- • Bose-Einstein condensation
Essential Formulas
Partition Function
$Z = \sum_i e^{-\beta E_i} = \text{Tr}(e^{-\beta H})$
Canonical partition function - central object in stat mech
Free Energy
$F = -k_B T \ln Z$
Helmholtz free energy from partition function
Fermi-Dirac Distribution
$\langle n_i \rangle = \frac{1}{e^{\beta(\epsilon_i - \mu)} + 1}$
Occupation number for fermions
Bose-Einstein Distribution
$\langle n_i \rangle = \frac{1}{e^{\beta(\epsilon_i - \mu)} - 1}$
Occupation number for bosons
Additional Video Resources
Susskind's Theoretical Minimum
Leonard Susskind's Statistical Mechanics lectures from Stanford's Continuing Studies program.
View LecturesJim Sethna's Online Textbook
"Entropy, Order Parameters, and Complexity" - modern interdisciplinary approach with exercises.
Free Online Book