SI2520 Nonequilibrium Statistical Mechanics 7.5 credits

Statistisk mekanik för icke-jämviktssystem

Nonequilibrium situations are far more common in nature than equilibrium ones. This course gives an introduction to the common ideas and different approaches for studying systems in statistical mechanics that are not in equilibrium, i.e.- with a time dependence in the description of the system. We begin with a review of the origin of irreversibility and the second law of thermodynamics, which are at the foundations of equilibrium statistical mechanics. Then various different techniques for studying non-equilibrium situations follows, which treat the problem on different levels of detail. The main part of the course considers effective descriptions in terms of stochastic processes, closely related to simple random walk problems. We also discuss the Boltzmann equation, which provides a microscopic framework for studying transport in dilute systems, and leads up to coarse-grained hydrodynamic descriptions on longer length scales. Finally, we discuss the linear regime close to equilibrium, where it is possible to obtain the linear response of the system from its equilibrium fluctuations, via the fluctuation-dissipation theorem.

Offering and execution

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Content and learning outcomes

Course contents *

• Irreversibility and the second law.
• Brownian motion: Random walks, Langevin equation, Fokker-Planck equation, Functional integrals.
• Stochastic processes in physics: Master equations, Generating functions, Doi formalism.
• The Boltzmann equation: The H-theorem and irreversibility. Conservation laws and hydrodynamics.
• Linear response theory: Kubo formula, Fluctuation-dissipation theorem, Onsager relations.

Intended learning outcomes *

After the course you shall

• have a broad overview of concepts, methods and approaches within non-equilibrium statistical mechanics.
• be able to model new physical situations using the methods exemplified in the course.
• be able to generalize and apply the methods to new problems.
• have gained insights into more advanced methods which touch upon modern research.

Course Disposition

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Literature and preparations

Specific prerequisites *

Recommended prerequisites: Introductory thermodynamics and statistical physics, and some quantum mechanics.

Recommended prerequisites

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Equipment

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Literature

Lecture notes will be made available.

Examination and completion

A, B, C, D, E, FX, F

Examination *

• TEN1 - Examination, 7.5 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade *

Solution of exercises, which are to be discussed with the examiner (TEN1; 7,5 university credits).

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SI2520

SCI/Physics

Physics

Education cycle *

Second cycle

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Contact

Jens Bardarson (bardarson@kth.se)

Ethical approach *

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Supplementary information

Reading course if there are few participants.