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Course, academic year 2018/2019
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Selected Chapters on Nonequilibrium Statistical Physics I - NTMF062
Title in English: Vybrané kapitoly z nerovnovážné statistické fyziky I
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: RNDr. Karel Netočný, Ph.D.
Annotation -
Last update: prof. RNDr. Jiří Podolský, CSc., DSc. (29.04.2019)
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 4th and 5th year of study and for doctoral students.
Literature -
Last update: RNDr. Karel Netočný, Ph.D. (12.05.2011)

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.

Requirements to the exam -
Last update: RNDr. Karel Netočný, Ph.D. (13.10.2017)

The exam is oral. The requirements correspond to the syllabus of the subject in the scope that was presented at the lecture.

Syllabus -
Last update: RNDr. Karel Netočný, Ph.D. (12.05.2011)
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.

 
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