Nonequilibrium Statistical Mechanics

Homepage for the course PH5081 Nonequilibrium Statistical Mechanics — NPTEL course by Prof. V. Balakrishnan with assistance from me.

Target Audience

It is an elective course in the M.Sc. as well as B.Tech. (Engg. Physics) curriculum.

Assessment

2 Quizzes	$25\times 2$	50
Final	$50\times 1$	50
Total		100

Course Notes

Official Course Content

Objectives: To introduce the fundamental statistical mechanics of systems away from thermal equilibrium, including time-dependent phenomena such as transport.

+ See course content

Course Content:

Linear Response Theory: Density operator, classical and quantum Liouville equations, response functions as correlators, generalized susceptibility. Fluctuation dissipation theorems, relaxation response relationships, Kubo-Green formulas, examples.

Langevin dynamics: Markov processes, Langevin equation, Fokker-Planck equation, Ornstein-Uhlenbeck process. Dynamic mobility, dispersion relations. Fokker-Planck equation in phase space, diffusion limit. Diffusion in a potential, Smoluchowski equation, diffusion in a magnetic field. Kramers' escape rate formalism, Memory kernel, frequency- dependent friction, generalized Langevin equation.

Dynamic critical phenomena: Time-dependent Ginzburg-Landau model, dynamic critical exponents. Glauber dynamics of Ising Spins.

Chemical kinetics: Reaction-diffusion systems. Turing and Hopf bifurcations, spatiotemporal patterns. Fitzhugh-Nagumo, Cahn-Hilliard and Kardar-Parisi- Zhang equations and applications. Asymmetric simple exclusion process.

Thermodynamics at the molecular level: Irreversibility paradoxes, Maxwell’s demon, Brownian ratchet, Brownian motors. Fluctuation Theorem, nonequilibrium partition identity, Crooks fluctuation theorem, Jarzynski equality.

Text Books:

1. R. Kubo, M. Toda and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer).
2. G. F. Mazenko, Nonequilibrium Statistical Mechanics (Wiley-VCH).
3. R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford).

Reference Books:

1. J. Keizer, Statistical Thermodynamics of Nonequilibrium Processes (Springer).
2. V. Balakrishnan, Elements of Nonequilibrium Statistical Mechanics (Ane Books).
3. B. H. Lavenda, Nonequilibrium Statistical Thermodynamics (Wiley).
4. R. M. Mazo, Brownian Motion: Fluctuations, Dynamics and Applications (Oxford).
5. P. Grindrod, Patterns and Waves: The Theory and Applications of Reaction- Diffusion Equations (Clarendon).
6. D. J. Evans and D. J. Searles, Fluctuation theorems, Adv. Phys. Vol. 51, pp. 1529-1585 (2002).
7. U. C. Tauber, Critical Dynamics (Cambridge).