Selected Chapters on Nonequilibrium Statistical Physics I - NTMF062
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Basic ideas and recent trends in non-equilibrium statistical mechanics. We discuss the irreversibility of
macroscopic dynamics in relation to the microscopic reversibility and the essential role played by the detailed
balance and its local generalization for understanding the behavior of open thermodynamic systems out of
equilibrium. We derive some symmetry relations for dynamical fluctuations and basic statistical properties of non-
equilibrium processes.
For the 1st and 2nd year of study and for doctoral students.
Last update: Podolský Jiří, prof. RNDr., CSc., DSc. (29.04.2019)
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Ústní zkouška Last update: Houfek Karel, doc. RNDr., Ph.D. (11.06.2019)
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C. Maes, K. Netočný, and B. Shergelashvili: A selection of nonequilibrium issues , Lecture notes in Mathematics 1970 (2009) 247-306. http://www.fzu.cz/~netocny/Documents/PrahaLN.pdf.
D. Chandler: Introduction to Modern Statistical Mechanics (Oxford University Press, 1978), Chapter 8.
Last update: Netočný Karel, RNDr., Ph.D. (12.05.2011)
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The exam is oral. The requirements correspond to the syllabus of the subject in the scope that was presented at the lecture. Last update: Netočný Karel, RNDr., Ph.D. (13.10.2017)
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Macroscopic irreversibility
Boltzmann equation for rarefied gas; H-theorem; Zermelo-Poincare and Loschmidt paradoxes; Kac model; macroscopic autonomy; Onsager-Machlup symmetry and thermodynamic arrow of time. Stochastic dynamics Formal construction of reduced dynamics from mechanical equations; detailed balance and the time-reversal symmetry; Markov jump processes; Kolmogorov generator and its spectral properties; path distribution. Systems coupled to heat bath Relaxation and thermodynamic processes; entropy production; minimal work principle, statistical distributions for work and heat; Jarzynski equation, quasistatic ("adiabatic") limit; fluctuation-dissipation theorem; Onsager regression hypothesis. Non-equilibrium stochastic processes Systems interacting with more baths; local detailed balance principle; entropy production as a measure of the time-reversal symmetry breaking; thermodynamic formalism for stationary fluctuations; Gallavotti-Cohen fluctuation symmetry; perturbative calculation of current cumulants. Thermodynamics of weakly non-equilibrium systems Green-Kubo linear response relations; Onsager reciprocities; McLennan stationary ensemble; minimum entropy production principle; time-symmetric fluctuations. Diffusion processes Diffusion limit of random walk; continuous Markov processes; overdamped and underdamped diffusion, Johnson-Nyquist noise; Onsager-Machlup theory of dynamical fluctuations. Last update: Netočný Karel, RNDr., Ph.D. (12.05.2011)
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