Non-Equilibrium Statistical Mechanics

Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Course Description

This course discusses the principles and methods of non-equilibrium statistical mechanics. Basic topics covered are stochastic processes, regression and response theory, molecular hydrodynamics, and complex liquids. Selected applications, including fluctuation theorems, condensed phase reaction rate theory, electron transfer dynamics, enzymatic networks, photon counting statistics, single molecule kinetics, reaction-controlled diffusion, may also be discussed.

Prerequisites

5.70 Statistical Thermodynamics with Applications to Biological Systems
5.73 Introductory Quantum Mechanics I
18.075 Advanced Calculus for Engineers

Textbooks

The following is a list of recommended textbooks that you may find useful for this course. No required readings will be assigned.

Groot, Sybren Ruurds de, and Peter Mazur. Non-Equilibrium Thermodynamics. Dover Publications, 2011. ISBN: 9780486647418.

Van Kampen, N. G. Stochastic Processes in Physics and Chemistry. Elsevier, 2007. ISBN: 9780444529657. [Preview with Google Books]

Boon, Jean-Pierre, and Sidney Yip. Molecular Hydrodynamics. McGraw-Hill, 1980. ISBN: 9780070065604.

Reichl, Linda E. A Modern Course in Statistical Physics. Wiley-Interscience, 1998. ISBN: 9780471595205.

Hansen, Jean-Pierre, and Ian R. McDonald. Theory of Simple Liquids. Elsevier Academic Press, 2006. ISBN: 9780123705358. [Preview with Google Books]

McQuarrie, Donald A. Statistical Mechanics. University Science Books, 2000. ISBN: 9781891389153.

Assignments

There will be 6 problem sets assigned. They will be graded.

Final Project

You will have to complete a final project at the end of the term. You will be given a set of problems to work on outside of class.

Grading

This course will be graded based on the following:

ACTIVITIES	PERCENTAGES
Class participation	10%
Four problem sets	50%
Final project	40%

Calendar

Please note: each chapter of lecture notes is multiple lectures, and each section is roughly equivalent to one week.

CHAPTER #	TOPICS	SUBTOPICS
1	Stochastic Processes and Brownian Motion	1.1 Markov Processes 1.1.1 Probability Distributions and Transitions 1.1.2 The Transition Probability Matrix 1.1.3 Detailed Balance 1.2 Master Equations 1.2.1 Motivation and Derivation 1.2.2 Mean First Passage Time 1.3 Fokker-Planck Equations 1.3.1 Motivation and Derivation 1.3.2 Properties of Fokker-Planck Equations 1.4 The Langevin Equation 1.5 Appendix: Applications of Brownian Motion
2	Non-equilibrium Thermodynamics	2.1 Response, Relaxation, and Correlation 2.2 Onsager Regression Theory 2.3 Response Response Theory and Causality 2.3.1 Response Functions 2.3.2 Absorption Power Spectra 2.3.3 Causality and the Kramers-Kronig Relations
3	Hydrodynamics and Light Scattering	3.1 Light Scattering 3.2 Navier-Stokes Hydrodynamic Equations 3.3 Transport Coefficients
4	Time Correlation Functions	4.1 Short-time Behavior 4.2 Projection Operator Method 4.3 Viscoelastic Model 4.4 Long-time Tails and Mode-coupling Theory