Statistical mechanics for non-equilibrium systems

Lecture notes, Spring 2015

These may be updated during the course, so please download and print them only when they are not greyed out anymore.

  1. The second law and the origin of irreversibility.
    If you want to learn more see. e.g., Joel L. Lebowitz (2008) Time's arrow and Boltzmann's entropy, Scholarpedia, 3(4):3448, Le Bellac: Ch 2.6., V. Ambegaokar and A.A. Clerk, Am. J. Phys. 67, 1068 (1999), R. Balian, Am. J. Phys. 67, 1078 (1999),  and J.L. Lebowitz, Physica A 263, 516 (1999).
  2. Brownian motion, random walks, and Langevin equation.
    (References: Reif: Ch. 15, Zwanzig: Ch. 1.)
  3. The Fokker-Planck equation.
    (References: Zwanzig: Ch. 2, Kubo: Ch. 2.4)
  4. Spectral density and the Wiener-Kinchin theorem.
    (References: Reif: Ch. 15; Kubo: 1.3)
  5. Functional integral methods.
    More reading: J. Cardy, "Scaling and Renormalization in Statistical Physics" (Cambridge, 1996), Ch. 10; Zinn Justin: "Quantum Field Theory and Critical Phenomena".
  6. Stochastic processes, Master equations.
    (van Kampen: Ch. 1-4; Reif: Ch. 15)
  7. Examples of stochastic processes.
    (Reif: Ch. 15; v Kampen Ch. 5-6)
  8. Long time behaviour.
    (van Kampen: Ch. 5; Kubo: Ch. 2.3)
  9. Generating functions and Doi formalism.
    (van Kampen: Ch. 5-6.  For the 2:nd quantized approach see M. Doi, J. Phys. A: Math. Gen. 9 1465-1477 (1976).)
  10. Deterministic equations and First passage problems.
    (van Kampen: Ch. 5-6; Zwanzig: Ch. 4.2)
  11. Kinetic theory and the Boltzmann equation.
    (Reif: Ch. 13-14; Le Bellac: Ch. 8)
  12. Linear response theory, the Kubo formula and causality.
    (Kubo: Ch 4; Le Bellac: Ch. 9)
  13. Fluctuation-dissipation theorem, Onsager relations.
    (Kubo: Ch 4; Reif: Ch 15)
  14. Irreversible thermodynamics.
    (Kubo: Ch 4; Reif: Ch 15)
  15. Fluctuation theorems far from equilibrium.
    Hundreds of papers have been written on these last years. See e.g., the review C. Bustamante, J. Liphardt and F. Ritort, Physics Today, 58, 43 (2005), E. Boksenbojm, B. Wynants, and C. Jarzynski, Phys. A Stat. Mech. Its Appl. 389, 4406 (2010) .

Reference litterature

Homework examination


Jack Lidmar    <jlidmar -at- kth.se> 2014-12-18