Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Qualitative comparison of equilibrium and nonequilibrium systems.
Review of thermodynamic ensembles, phase space density, Liouville
equation.
- Langevin equation, fluctuation-dissipation theorem, velocity
autocorrelation.
- Master equations, Chapman-Kolmogorov equation, Kramers-Moyal
expansion, Discrete Markov processes, solution of Master equation,
stationary distribution, detailed balance, Einstein-Smoluchowski
equation.
- Fokker-Planck equation, Ornstein-Uhlenbeck (OU) distribution, the
diffusion equation. Diffusion in three dimensions, Diffusion in a
finite region, reflecting and absorbing boundaries. Brownian motion,
Wiener processes, relationship between OU and Wiener processes,
Survival probability, mean first-passage time.
- Diffusion in a potential, Langevin equation in an external potential,
Kramer's equation, Brownian oscillator, Smoluchowski equation,
Kramer's escape rate. Diffusion in a magnetic field.
- Green-Kubo formulas, Dynamic mobility, power spectral density,
Wiener-Khinchin theorem, white and colored noise.
- V. Balakrishnan, Elements of Nonequilibrium Statistical
Mechanics, Ane Books, New Delhi (2008).
- R. Zwanzig, Nonequilibrium Statistical Mechanics, Oxford
University Press (2004).
- N. G. van Kampen, Stochastic Processes in Physics and
Chemistry, North Holland Amsterdam (1985).
- H. Risken, The Fokker-Planck Equation: Methods of Solution and
Applications, Springer-Verlag Berlin (1996).
