PHYS 425: Statistical and Thermal Physics (Fall 2008)

This is a lecture course designed to provide a solid grounding in both thermodynamics and statistical physics. While typically a senior level course, interested juniors are encouraged to enroll, as are first year graduate students who would like to review the material.
  • Logistical details
  • Introductory remarks: why you should care about this.
  • What is statistical and thermal physics?
  • Structure and grading
  • Honor code issues
  • Course outline
  • References
  • Resources on the web

  • Logistical Details

    Instructor:  Prof. Douglas Natelson
    Office:  Space Sciences Bldg., Room 329
    Contact information:  x3214,
    TAs:  Liang Zhao, Changhao Wang
    Contact information:, Chanhao Wang
    Course meets:  Tu-Th, 13:00-14:20, HZ 210
    Office hours:  Mon., 10-12.  For additional time, my door is open, but you may want to call ahead to make sure I'm around.
    Text:  The official textbook is Statistical and Thermal Physics by Reif, and is available in the campus bookstore.  Note that I will supplement this book substantially with additional material from a variety of references - see below. PLEASE, I ENCOURAGE YOU TO BUY A USED COPY OF THIS BOOK. I picked it because it's got nice explanations of some key concepts, and it's a real shame that the price is so absurd.

    If you have a documented disability that will impact your work in this class, please contact me to discuss your needs. Additionally, you will need to register with the Disability Support Services Office in the Ley Student Center.

    Introductory remarks:  Why you should care about this.

    Statistical physics is one of the most amazing intellectual developments of the last hundred and fifty years.  It has its roots in classical thermodynamics, the study of "heat flow".  From those modest beginnings, it now forms the basis of our understanding of solids, liquids, and gases.  Without statistical physics, semiconductor-based high technology would not exist, we wouldn't understand why outer space glows at 2.7 Kelvin, and Einstein would not have had a PhD thesis topic.  Insights from statistical physics have guided the development of key ideas in high energy physics while simultaneously showing the unity underlying such apparently diverse phenomena as ferromagnetism, the liquid-vapor transition, and the orientation of liquid crystals.  Statistical physics ideas are deeply relevant to frontier research in a number of areas, from physical chemistry to quantum computation to biophysics, and the subject itself continues to be explored actively.  To summarize, familiarity with statistical and thermal physics ideas is essential to calling yourself scientifically literate.

    Learning statistical and thermal physics is challenging, and so is teaching it.  This subject is vast, the concepts are new, and, like quantum mechanics, fluency in statistical physics requires an intuition all its own.  Also like quantum mechanics, there are many problems that are easy to state and extremely difficult to solve exactly.  In this course you'll gain experience with approximations and models, and learn about their regimes of validity.  I often refer to this kind of reasoning as "thinking like a physicist".  The only way to really get an understanding of this subject is to work many problems spanning the concepts involved.

    Because of the limited time available in a one-semester course, I can't cover everything I'd like.  Also, traditional treatments such as the one in the official textbook (Reif) were typically written in the 1960's, and omit some of the most profound developments in this area in the last forty years.  Therefore, rather than proceeding straight through Reif, I am going to present the subject in a different order, while augmenting the text with additional course materials from various sources as necessary.  I want to make sure you get a solid grounding in the fundamentals of the field, while still having a chance to sample some of the more recent developments.

    The course will be challenging.  You'll be seeing lots of new concepts, some familiar and some not, and we'll be moving at a good clip.  Please try and read the recommended material before class - it'll make your life easier later.  Similarly, don't delay on starting the problem sets.  You'll find them easier if you mull them over for a while rather than waiting until the last minute.

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    What is statistical and thermal physics?

    As the name implies, statistical and thermal physics deals with the use of statistical methods to understand the behavior of complex, many-particle systems; in particular, this machinery was originally developed to understand quantitatively the ideas of temperature, heat flow, and irreversibility.

    Why do we need a statistical approach?  You already know that general interacting problems involving more than two particles seldom have exact solutions.  On the other hand, the air in this room (on the order of 1024 particles) seems to be in a well-defined "equilibrium state" that we're accustomed to characterizing by a small number of parameters (temperature, pressure, volume).  Despite the fact that we can't keep track of the movements of each particle individually, we can still make predictions about some sort of average behavior of the whole set of particles.  Further observations tell us that fluctuations away from the equilibrium state seem to be unnoticeably small, despite the fact that there's nothing in the microscopic laws obeyed by each particle to prevent all the gas molecules from ending up in the upper half of the room at the same time.  Similarly, you know from experience that "heat energy" flows from hot objects to cold objects spontaneously, and never the reverse.  Statistical and thermal physics aims to examine the properties of "large" systems, and explain observations like those described above.

    The machinery of statistical physics is extremely powerful because of its generality.  The same formalism used to understand the classical ideal gas can be applied to understanding such highly quantum mechanical problems as electrons in metals, black body radiation, Bose-Einstein condensation, and the behavior of ferromagnets.

    By the end of this course, you should be able to answer questions like:

    Statistical physics and the phenomena it explains are the prime example of emergent properties, rich and complex properties that occur in systems with many degrees of freedom, even when those microscopic degrees of freedom obey simple rules (i.e. Newton's laws).  The phrase that best describes this is "More is different", the title of an article by P.W. Anderson (Nobel 1977) (Science 177, 393 (1972)).  The fact that the collective properties of matter are so amazing and so difficult to deduce a priori from the underlying simple rules is the reason statistical (and condensed matter) physics continues to be a hot topic of current research.

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    Structure and grading

    The course will consist of two 80-minute lectures per week.  There will be weekly problem sets, given out on Thursday and due the following Thursday at the beginning of class.  Late work will only be accepted if due to illness or emergency - I want a legitimate excuse.

    Hurricane Ike disruption - Hurricane Ike has disrupted the course schedule a bit. Problem Set 2 will be due Tuesday, September 23, 2008. Problem Sets 3 and 4 will be combined and compressed, and will be handed out Tuesday, September 23, due Thursday, October 2.

    Understanding the material is at least as important as getting a numerically or formulaically correct answer to the problem. If your reasoning isn't obvious, please write little explanations of what you're doing and why, so partial credit can be assigned in a reasonable way.

    Every week I will also hand out additional problems in addition to those that make up the problem set.  These problems will collectively be known as the question bank, and will provide additional practice for you as the semester progresses.  You don't have to do these, and solutions to them will not be handed out.  However, I will tell you that approximately 1/3 of the final exam will be problems from the question bank.  You probably don't want to leave all these for the end of the semester....

    The problem sets are not pledged.  I encourage you to discuss the problem sets and question bank material with each other.  You may give each other guidance and advice on problem solving approaches, and you may compare solutions to check your work.  However, you may not copy solutions from another student, and the problem sets you submit must be entirely your own work and your own words.  If you used a book, you must cite the relevant material.  If you collaborated strongly with other students, cite them as well - this is intellectual honesty. Googling around to find solutions is unacceptable and (trust me) not worth the effort.

    There will be two exams in the course.  The overall grading will be:

    40% homework
    30% first exam (takehome, handed out Thu. October 2, due back Thu. October 9)
    30% final exam (also takehome,  scheduling TBA.)
    The takehome exams will be pledged open-notes (yours only!), open-Reif-only tests.

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    Honor Code issues

    All work on exams and problem sets is subject to the Honor Code.  I take the Honor Code seriously, and I expect you to do the same.  The homework and exam situations have been described above.  If you have any questions about this, raise them with me at the beginning of the course.

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    Course Outline

    This is a brief outline of topics to be covered in the course.  A detailed breakdown as well as a schedule of classes is available here, and will be updated as the semester progresses.  We may not get to everything, but I intend to try.
    I. Overview and introduction

    II.  Probability and necessary mathematics

    Probability, distributions, counting, partial derivatives
    III.  Basics of classical thermodynamics
    States, macroscopic vs. microscopic, "heat" and "work",
    energy, entropy, equilibrium, laws of thermodynamics
    IV.  More classical thermodynamics
    Equations of state, thermodynamic potentials, temperature, pressure,
    chemical potential, thermodynamic processes (engines, refrigerators),
    Maxwell relations, phase equilibria.
    V.  Statistical mechanics - the formalism.
    Counting states, ensembles (microcanonical, canonical, grand canonical),
    the partition function and its applications, fluctuations from equilibrium,
    VI.  Magnetic systems
    Paramagnetism, ferromagnetism, adiabatic cooling, susceptibility & correlations,
    mean field theory, Ising model.
    VII.  Gases
    Classical ideal gas (Maxwell distribution), Bose gas (mode-counting,
    photons, phonons, BEC), Fermi gas (degeneracy pressure, heat capacity),
    van der Waals and "real" gases.
    VIII.  Phase transitions
    Landau theory, scaling, renormalization, solution to 1D Ising
    IX.  Transport
    Diffusion, Brownian motion, Boltzmann equation.
    X.  Special topics
    Arrow of time, fluctuation-dissipation theorem, nonequilibrium systems,
    granular media, the density matrix

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    Other statistical and thermal physics texts:

    H.C. Callen.  Thermodynamics and an Introduction to Thermostatistics, 2nd ed., Wiley.  An excellent treatment of classical thermodynamics, though the statistical mechanics portion is tacked on.

    C. Kittel and H. Kroemer.  Thermal Physics, 2nd ed., Freeman.  Another standard, this one more on the statistical physics side.  It uses rather nonstandard notation in places, but has great problems.

    F. Mandl.  Statistical Physics, 2nd ed., Wiley.  Pretty decent.  Strong in thermodynamics.  Needs more exercises.

    R. Baierlein.  Thermal Physics, Cambridge University.  Haven't used it; supposed to be a decent undergrad book.

    D.V. Schroeder. Introduction to Thermal Physics, Addison Wesley.  I've looked through it;  looks like a decent undergraduate book.

    D.A. McQuarrie.  Statistical Mechanics, University Science.  Very good, though quite advanced.  Looks at things more from the physical chemistry point of view.

    D.L. Goodstein. States of Matter, Dover.  Excellent, but somewhere between a stat mech and a solid state text.  It's very readable, and a very good deal since it's a Dover book.

    L.D. Landau and E.M. Lifshitz. Statistical Physics Part 1, 3rd ed., Pergamon.  A classic.  Very dense, borderline graduate level.

    R.P. Feynman.  Statistical Mechanics: a set of lectures, Addison Wesley.  Another classic.  Graduate level, good for understanding the density matrix.

    P.M. Chaikin and T.C. LubenskyPrinciples of Condensed Matter Physics. Cambridge University.  Has very good chapters on phase transitions.  Avail. in paperback, so it's not absurdly expensive.

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    Resources on the web

    Statistical and thermal physics sites
    The STP Project - A project helmed by two faculty members (Harvey Gould at Clark University and Jan Tobochnik at Kalamazoo College) to reform the teaching of statistical and thermal physics.  Includes a draft textbook, and a very nice compendium of web resources. - A University of Pennsylvania physical chemistry look at the Maxwell-Boltzmann distribution, including applets.. - Some applets related to black body radiation. - A statistical physics timeline, for history buffs. - The thermometry research group at NIST, actively trying to improve our understanding and standards of temperature, particularly below 1 K. - an applet that shows an example of macroscopic irreversibility from microscopically reversible laws of motion in the presence of infinitesmal perturbation. - an applet that shows the percolation phase transition. - another applet, this one showing a numerical approach to the 2d ising model.

    Good physics-related websites  - Cornell e-print server - the latest hot results, but no peer review.... - IBM Research - lots of neat topics - Very cool java applets for solid state physics! - More and different java applets for solid state physics. - Another java-driven physics site, though at a lower level. - University of Oregon's "virtual lab", another collection of applets.

    Statistics websites - The Rice University virtual statistics laboratory.  Very cool. - an applet for demonstrating the "Monty Hall" problem. - an applet by the same author for demonstrating the Central Limit Theorem. - a large number of statistics demo applets.

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    Last modified 08/11/08 by