David Tong: Kinetic Theory

David Tong: Lectures on Kinetic Theory

This is a graduate course on topics in non-equilibrium statistical mechanics, covering kinetic theory, stochastic processes and linear response. It is aimed at masters students and PhD students. The full set of lecture notes are around 100 pages. They can be downloaded below. Please email me if you find any typos.


A first course on statistical mechanics and thermodynamics can be found here.


  • 1. Things Bumping Into Other Things:   PDF
    Introduction; Basics of Collisions; Mean Free Path; Scattering Time; Basics of Transport; Diffusion; Viscosity; Thermal Conductivity.
  • 2. Kinetic Theory:   PDF
    BBGKY Hierarchy, Boltzmann Equation, Equilibrium and Detailed Balance, The H-Theorem, Ideal Fluids, Relaxation Time Approximation; Thermal Conductivity and Viscosity Revisited; Navier-Stokes Equation; Sound Waves.
  • 3. Stochastic Processes:   PDF
    Brownian Motion; The Langevin Equation; Diffusion; The Einstein Relation; Noise Distributions; The Fokker-Planck Equation; Kramers-Chandrasekhar; Path Integrals, Stochastic Calculus.
  • 4. Linear Response:   PDF
    Sources, Observables and Response Functions; Causality and Analyticity; Kramers-Kronig Relation; Dissipation; Kubo Formula; Fluctuation-Dissiptation Theorem, Response in Quantum Field Theory

Kinetic Theory on the Web