**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, Maxwellâ€™s demon, Brownian ratchet, Brownian motors. Fluctuation Theorem, nonequilibrium partition identity, Crooks fluctuation theorem, Jarzynski equality.

**Text Books:**

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

**Reference Books:**

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