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Course, academic year 2018/2019
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Selected Chapters on Nonequilibrium Statistical Physics II - NTMF068
Title in English: Vybrané kapitoly z nerovnovážné statistické fyziky II
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2014
Semester: summer
E-Credits: 3
Hours per week, examination: summer 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)
The second part is devoted to some aspects of the time-scale separation, which is responsible both for the Markovian behavior of relevant ("slow") degrees of freedom for small open systems and for the autonomous dynamics of macroscopic systems. We also discuss basic stochastic models of interacting particles, their macroscopic limit and fluctuations. For the 4th and 5th year and for doctoral students.
Course completion requirements -
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.

Literature -
Last update: T_UTF (17.05.2012)

H.-P. Breuer and F. Petruccione: The Theory of Open Quantum Systems (Oxford University Press, 2002).

B. Derrida: Non equilibrium steady states: fluctuations and large deviations of the density and of

the current (2007). .

G. Jona-Lasinio: From fluctuations in hydrodynamics to nonequilibrium thermodynamics, Prog. Theor. Phys. Suppl. 184 (2010) 262-275. .

Syllabus -
Last update: T_UTF (13.05.2011)
Markovian subdynamics
Slow versus fast degrees of freedom; derivation of the Smoluchowski equation for overdamped diffusion; thermal activation and noise-induced decay of metastable states - Arrhenius and Kramers theories; reduced dynamics of quantum subsystems - Davies weak-coupling theory, quantum Markov processes, rotating-wave approximation.

Stochastic many-body models
Open interacting particle systems as mesoscopic models for diffusion; heat conduction in a chain of coupled oscillators with open ends; Kipnis-Marchior-Presutti model of transport.

Autonomous macroscopic dynamics
Kinetic and diffusive (or "hydrodynamic") scaling; derivation of macroscopic diffusion equations from stochastic exclusion models; local thermodynamic equilibrium; equations of linear non-equilibrium thermodynamics.

Macroscopic fluctuations
Generalized Onsager-Machlup theory of dynamical fluctuations; Onsager-Machlup symmetry breaking; non-equilibrium entropy from typical histories of large fluctuations, Hamilton-Jacobi equations for the entropy, current fluctuations, vortex patterns in two-dimensional transport.

 
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